The 20-year-old Dane enjoyed a strong campaign last year, winning one title and reaching the finals of the Masters in Rome and Monte-Carlo.
Rune got this season off to a good start too, reaching the final of the Brisbane International, which he lost in straight sets to Grigor Dimitrov.
World number eight Rune will be aiming to go one further at the Australian Open, with his campaign starting against Yoshihito Nishioka.
While Opta's predictive model gives Rune just a one per cent chance of going all the way in Melbourne, he is confident he can claim his maiden major title this year.
"I believe that I am a contender to win a grand slam next year," he told Stats Perform.
"It's going to take a lot of work, but I've sacrificed a lot and I'm trusting the process every day and coming out of my comfort zone.
"Every practice is physical and trying to improve mentally also so if I do better next year it won't surprise me."
It is not just the four majors on the cards this season, but a potential medal at the Paris Olympics.
Rune added: "Yeah, it's going to be a very exciting season. There's a lot of chances next year for grand slams, for the Olympics, and I'm going to go for it.
"I'm going to go to every tournament that I can.
"[The Olympics mean] a lot, everything. With the grand slams, it's the biggest thing in tennis. It's every fourth year, so it's very rare.
"I think if you ask me whether I'd rather win a grand slam or the Olympics, I think I'll still say a grand slam, but the second thing I would say is the Olympics. It's a massive event."
Rune's All England Club campaign was ruthlessly ended by Novak Djokovic in the fourth round, beaten in straight sets by the eventual finalist.
The Dane gave himself little time to lick his wounds and has quickly returned to the court and returned to form with his debut in Hamburg.
Looking for his first ATP Tour title of the year, the second seed followed up a straight-sets win over Fabian Marozsan by defeating Marco Trungelliti 6-4 6-3.
"It's been very intense since Wimbledon," Rune said. "I only had one day off, actually.
"I was like, 'I don’t want to rest, I want to go straight back to practice', because I was very disappointed.
"I went straight back to work on the things that needed to be done, and now I have the chance to train those things in matches."
Next up will be Arthur Fils, who booked his last-eight place by beating 2023 Hamburg finalist Laslo Djere 7-6 (7-3) 6-2.
Top seed Alexander Zverev remains a threat in the top half of the draw, however, and he will face Zhang Zhizhen in the quarters.
Rune, who withdrew from the Olympics due to a wrist injury, had been set to face Milos Raonic in the first round.
However, Raonic withdrew just moments before the match was due to start, so lucky loser Bautista Agut filled in.
It left Rune having to swiftly adapt to a new opponent, but despite a wobble in the second set, the Dane was generally in control throughout Tuesday's contest.
"It was a challenge for sure," Rune said. "It's never easy coming back after a little break — not the longest break, but for me, I'm very young and luckily I haven't been injured much. It was difficult but I think I managed to find the rhythm quickly.
"It was kind of tricky. It's two completely different game styles. I kind of had to adjust from one tactic to another in five minutes. Luckily, I played Bautista before so I had a clue, and obviously he's been on Tour for many years, so I know him very well.
"It was not easy. I was expecting a big server and trying to manage to get in the rallies with Milos, and now it was a completely different story. I needed to attack much more and play on my terms."
Next up for Rune, who has won 13 of his 15 opening-round matches this season, is a tie against Pablo Carreno Busta.
Data Debrief: Scandi style
Since the format’s inception in 1990, world number 17 Rune is now the fourth Scandinavian player to claim 30+ wins from an opening 50 ATP Masters 1000 matches.
He joins Stefan Edberg (41), Magnus Gustafsson (32) and Casper Ruud (31) on that list.
Appearing as the top seed at an ATP event for the first time, Rune had lost both his previous meetings with Huesler, including last season's Sofia Open.
However, the world number nine made it third time lucky to set up a last-eight clash with Gregoire Barrere, who beat Nikoloz Basilashvili in straight sets.
Meanwhile, third seed Borna Coric is now just one win away from securing a return to the top 20 in the ATP rankings. The world number 23 – and reigning Cincinnati champion –saw off Arthur Rinderknech 6-3 7-5.
Although, there was no joy for Alejandro Davidovich Fokina. The fifth seed was ousted 6-3 6-3 by world number 70 Quentin Halys, who claimed only his second top-50 career win in 20 attempts.
Seventh seed Emil Ruusuvuori was also eliminated in straight sets by Maxime Cressy, but Lorenzo Sonego overcame Filip Krajinovic to book a quarter-final date with Jannik Sinner.
Rune has fallen from a high of four down to number 15 in the ATP rankings and was unable to hold on to a lead in his match with Thompson in London.
Australian Thompson fought back to prevail 4-6 7-6 (7-4) 6-3 in an entertaining encounter against the seventh seed.
Rune made the semi-finals at Queen's and the quarter-finals of Wimbledon last year, but is now seriously lacking momentum as the third grand slam of 2024 fast approaches.
Elsewhere at the ATP 500 event, third seed Grigor Dimitrov is safely through after cruising past Adrian Mannarino 6-1 6-2 in only 63 minutes.
Dimitrov will face either Sebastian Korda or Karen Khachanov in the last 16.
Top seed and defending champion Carlos Alcaraz starts his campaign against Argentine Francisco Cerundolo on Tuesday.
That is also when Thompson’s compatriot and last year’s runner-up Alex de Minaur begins his tournament with what could be a testing clash against Italian Lorenzo Musetti.
Data Debrief: Thompson's serve sees off Rune
In the first career meeting between the two players, both Rune and Thompson were strong on serve. The three sets only produced two breaks – one from each player – in a battle that topped the two-hour mark.
Thompson came into the tournament on a five-match losing streak, but has often impressed on grass, with this being his 64th career win on the surface.
He had eight aces to just one double fault and crucially won 69 per cent (20/29) of his second-serve points, affording Rune just one break-point opportunity across the whole match.
Thompson added 27 winners and could face home hope Andy Murray next round if the Briton can defeat Alexei Popyrin.
As for Dimitrov, he recorded 28 winners and only five unforced errors in his impressive win over Mannarino. Having made the quarter-finals at the French Open, the Bulgarian looks poised to enter Wimbledon in good form.
The 19-year-old defeated Djokovic 3-6 6-3 7-5, fending off the six-time champion at the indoor event to earn a place in the top 10 for the first time, becoming the first Danish man to reach such heights.
Rune becomes the first player since the ATP rankings were launched in 1973 to have beaten five top-10 players in the same tournament, other than at the season-ending ATP Finals.
His scalps on the route to his maiden Masters 1000 final included Hubert Hurkacz, Andrey Rublev, Carlos Alcaraz – who retired when trailing in their quarter-final – and Felix Auger-Aliassime.
Now Rune can add last year's Paris champion Djokovic to that list, defeating the 21-time grand slam winner who had described his young opponent as the future of tennis on the eve of the final.
Rune becomes the youngest Paris Masters champion since an 18-year-old Boris Becker triumphed in 1986, and he did it the hard way too, coming from behind after Djokovic made the stronger start.
Djokovic broke Rune's serve in the fourth game to lead 3-1 and take an early grip, soon seeing out the opening set.
Yet Rune charged 3-0 ahead in the second and grew in confidence. There was even a Djokovic-like raised fist after getting the better of his illustrious rival in one thrilling rally
Djokovic roared ahead in the decider, but not intimidated by the occasion, Rune struck back to recover the early break.
Rune then broke to lead 6-5, as his Serbian opponent became erratic.
Nobody beats Djokovic without a fight though, and the 21-time grand slam winner had six chances to break back in the next game.
Rune survived them all and clinched victory on his second match point when Djokovic, who had been chasing a record-extending 39th ATP 1000 title, netted on the half-volley.
Addressing Rune in an on-court interview, Djokovic said: "You absolutely deserve this victory. What an amazing week you had.
"I'm not happy that you beat me, but on the other hand I'm happy for you because I like your personality, I think you're a very dedicated guy that loves tennis and puts a lot of hours into hard work.
"It's paying off for you, and I'm sure the future is bright for you and your team, so congratulations."
Rune, who is working with Serena Williams' former coach Patrick Mouratoglou, said: "This must be my favourite tournament now, I really enjoyed my time here."
Still just 19, Rune added to his maiden crown in Munich five months ago with a 6-4 6-4 triumph over world number five Tsitsipas in a match lasting 95 minutes.
Tsitsipas, who was seeking a 10th ATP title and a third this season, had not dropped a set in his previous three matches en route to the final.
However, he was broken in the third game of both sets against Rune, who is the second teenager after Carlos Alcaraz to win multiple ATP titles in 2022.
Rune fired 20 winners and saved the only break point he faced – that coming in the sixth game of the second set – on his way to becoming the first Danish champion in this event.
"It was an unbelievable match from my side," Rune said in his on-court interview. "I knew it was going to be difficult, but I just tried to stick to the game plan.
"I had to play my best tennis today, and it was good that I could find the level. I am super happy. It was very close to perfection.
"I was making a lot of returns and playing pretty well behind my serve. Stefanos is an amazing player, who always makes it difficult. It was a super fun match to play."
Rune – the fifth seed for the tournament in Bulgaria – required two tie-breaks to clinch victory in his first meeting with Van Rijthoven on the ATP Tour, eventually claiming a 7-6 (7-2) 7-6 (8-6) win.
After the match, Rune expressed his relief at avoiding a third set, saying: "I didn't want to go to three sets. If it [had happened], I was going to fight for sure and try to take it in three, but I'm very happy to finish in two."
Meanwhile, eighth seed Oscar Otte beat Dragos Nicolae Madaras 6-3 6-2, and Portugal's Nuno Borges overcame Mirza Basic in three sets to tee up a meeting with defending champion and top seed Jannik Sinner.
In Tel Aviv, seeds Aslan Karatsev and Tallon Griekspoor fell at the first hurdle with three-set reverses to Tomas Martin Etcheverry and Vasek Pospisil, respectively.
Etcheverry rallied after Karatsev took a second-set tie-break in comprehensive fashion to post a 6-2 6-7 (0-7) 6-4 win, while lucky loser Pospisil stunned Griekspoor for a 4-6 7-6 (7-3) 7-5 triumph.
Fifth seed Botic van de Zandschulp fared better, however, dispatching Joao Sousa 6-2 6-3 after producing a top-class display of serving.
The Dutchman will meet Britain's Liam Broady in the next round after he recorded a straight-sets win over Hamad Medjedovic.
The 2022 US Open and French Open runner-up had struggled past Guido Andreozzi in the first round and followed up that up with a 7-5 2-6 7-6 (7-5) loss to Daniel.
The Japanese qualifier, ranked 125th in the world, won in just under three hours, winning the final three points of the deciding tie-break after Ruud led 5-4.
Ruud had more winners (38-32) but committed 30 unforced errors compared to Daniel's 12.
Taylor Fritz cruised into the last eight with a 6-4 6-4 win over Canada's Denis Shapovalov, setting up a quarter-final with sixth seed Francis Tiafoe, who eased past Feliciano Lopez 6-2 7-6 (8-6).
Fourth seed Holger Rune was too strong for Nuno Borges 6-0 6-2 inside an hour, while eighth seed Alex De Minaur crushed Jacopo Berrettini in just over an hour 6-1 6-0.
Top seed Lorenzo Musetti was a surprise second-round loser at the Chile Open with Jaume Munar triumphing 6-4 6-4 in one hour and 31 minutes.
Fourth seed Diego Schwartzman also bowed out, going down 6-4 4-6 7-6 (7-2) to local Nicolas Jarry.
Jarry will face Yannick Hanfmann in the quarter-finals, while Munar will take on Thiago Monteiro.
The Russian 14th seed prevailed 7-6 (7-4) 6-4 over Tsitsipas in one hour and 34 minutes, powering 25 winners and making only nine unforced errors, compared to the Greek's 14.
Khachanov's triumph ended a winless 0-6 head-to-head record against Tsitsipas, while it also snapped his own 23-match losing streak against top-10 opponents.
The Russian, who also made this year's Australian Open semi-finals, has qualified for four of his six tour-level events this year.
Khachanov will take on 25th seed Francisco Cerundolo in the quarter-finals, with the Argentinian fighting back to get past Lorenzo Sonego 3-6 6-3 6-2 in just over two hours.
Defending champion and top seed Carlos Alcaraz had less trouble against Tommy Paul, cruising into the quarter-finals with a 6-4 6-4 victory.
Alcaraz won the winners' count 24-9, setting up a quarter-final clash with ninth seed Taylor Fritz, as the Spanish 19-year-old chases a rare Sunshine Double, having won last week's Indian Wells Open.
Fritz progressed after getting past seventh seed Holger Rune 6-3 6-4 in 86 minutes, sending down eight aces and 22 winners for the match.
Fourth seed Daniil Medvedev played late into the evening after a lengthy rain delay in Miami, but made light work of Quinten Halys 6-4 6-2, triumphing just past 1:30am local time.
Medvedev, who is into his third straight Miami quarter-final, will face American qualifier Christopher Eubanks in the last eight after he got past Frenchman Adrian Mannarino 7-6 (7-2) 7-6 (7-5) in another rain-delayed contest.
Italian 10th seed Jannik Sinner knocked off sixth seed Andrey Rublev 6-2 6-4, advancing to face Emil Ruusuvuori after he beat Botic van de Zandschulp 4-6 6-4 7-5.
The trio, who have combined for a total of 64 men's singles grand slam titles across a near-two-decade-long period of dominance, have come to define the sport's modern era.
Federer retired last year and while Nadal and Djokovic continue, both are well into the twilight of their careers, despite astonished continued success.
Del Potro, the 2009 US Open winner, also retired in 2022, and he thinks the trio's dominance is unlikely to be replicated going forward, even though he sees Carlos Alcaraz, Jannik Sinner and Holger Rune as three players who could possibly go on to enjoy great success.
"The only thing I lacked was being number one [in the ATP Rankings]," he said. "It was always a dream, and I always worked for it. I never made it because there was either Federer, or Nadal, or Djokovic.
"When I look at the rankings and the years of my career and who was fighting to be number one I see that it was beautiful that these were the ones who didn't let me make it, this dream."
"One day, the big three will end. We have Carlos Alcaraz, Jannik Sinner [and] Holger Rune, other young people who will mark the circuit.
"But for me, [for] many years, [it was] the big three. There will not be anything similar."
Del Potro reached a career high-mark of third in the ATP Rankings in 2018, with Andy Murray the only man other than Nadal, Federer or Djokovic to top the charts between 2005 and 2021.
Thiem, a 2019 winner at the tournament in his home country, prevailed 6-4 6-2 in Kitzbuhel.
He will next face compatriot Sebastian Ofner as he seeks a first title since his grand slam breakthrough at the US Open in 2020.
Ofner came from a set down to beat former world number seven Richard Gasquet 1-6 7-5 7-5.
Meanwhile, seventh seed Pedro Martinez saved six out of six break points en route to a 7-6 6-3 victory over Chilean Nicolas Jarry.
At the Croatia Open in Umag, Bernabe Zapata Miralles set up a round of 16 meeting with third seed Holger Rune by beating Croatian Dino Prizmic, who retired when facing a 6-4 3-0 deficit.
Alex Molcan is safely through to the next round after defeating Duje Ajdukovic, while French 23-year-old Corentin Moutet cruised to a straight-sets victory over sixth seed Daniel Altmaier.
Thiem was on the brink of being knocked out by the top seed in Antwerp, but fought back to win 3-6 7-6 (11-9) 7-6 (7-4).
The 2020 US Open champion fended off all three match points in a second-set tie-break to take a thrilling quarter-final the distance and then came out on top in another breaker to advance.
Thiem will do battle with Sebastian Korda for a place in the final after the American emphatically defeated eighth seed Yoshihito Nishioka 6-0 6-2.
Richard Gasquet moved into the last four at the expense of David Goffin and will face Felix Auger-Aliassime, who came from a set down to beat Dan Evans.
Matteo Berrettini remains in the hunt to win the Tennis Napoli Cup on home soil after a 6-2 6-3 quarter-final triumph over Taro Daniel.
Top seed Pablo Carreno Busta crashed out in Italy, losing 7-5 6-2 to Miomir Kecmanovic, who will face Lorenzo Musetti after he got the better of Daniel Elahi Galan. Mackenzie McDonald will come up against Berrettini after getting past Zhang Zhizhen.
Stefanos Tsitsipas sealed a Stockholm Open semi-final spot with a 7-5 6-3 win over Mikael Ymer and will take on Emil Ruusuvuori, who eliminated Frances Tiafoe.
Holger Rune and Alex de Minaur meet in the other last-four match in the Swedish capital following wins over Cameron Norrie and Denis Shapovalov respectively.
With his 20th birthday approaching on May 5, world number two Alcaraz will have the chance on Sunday to land his ninth ATP title as a teenager.
Alcaraz crushed the hopes of first-time Barcelona semi-finalist Dan Evans, racing to a 6-2 6-2 victory over a player who was seeking to become the first British finalist at this tournament.
Earlier, Tsitsipas, who had not dropped serve en route to the semi-finals, had to dig deep for a 6-4 5-7 6-3 victory against Lorenzo Musetti, the Italian who beat Novak Djokovic in Monte Carlo last week.
Greek star Tsitsipas bizarrely has a 0-9 record in finals at ATP 500 level, the tier at which this tournament sits, despite having won two of his six title matches in elite ATP 1000 events.
Alcaraz will start as a firm favourite in the final. He holds a 3-0 career head-to-head lead over Tsitsipas from their past meetings, including a three-set win in the Barcelona quarter-finals last year.
That was a stormy encounter, with Alcaraz taking exception to almost being hit by a shot from Tsitsipas at the end of the opening set, so the rematch could be one to savour.
"It's so special to play a final here in Barcelona, a tournament I love playing," Alcaraz said on Prime Video. "I came to watch this tournament when I was very, very young, and I played for this club when I was 12, 11. I love this club, I love this tournament, and it's so special to have the chance to lift the trophy here again.
"Last year [against Tsitsipas] we had a spicy match, but I know he's a really nice guy off the court."
At the BMW Open in Munich, it was much the same story on Saturday.
Defending champion Holger Rune, another 19-year-old with a birthday approaching, in his case on April 29, earned another shot at the title.
Rune set up a Sunday showdown against Botic van de Zandschulp, in what will be a repeat of last year's final.
A resilient Rune lived up to his top seeding by ending Christopher O'Connell's fine run, which included a win against Alexander Zverev at the last-16 stage.
The 6-3 6-2 outcome masked the fact Rune saved eight break points as unseeded world number 82 O'Connell threatened to make it a tighter contest on the scoreboard than it turned out to be.
Van de Zandschulp then scored a fine win in the second semi-final as the Dutch fourth seed got the better of American second seed Taylor Fritz, winning 6-4 7-6 (7-2)
Last year's trophy match ended in disappointment when Van de Zandschulp retired due to chest pains during the first set, with Rune saying it was "probably the worst way to win a final".
Rune has three ATP titles to his name, with 27-year-old Van de Zandschulp yet to lift a singles trophy.
Seeded second and third respectively, Tsitsipas and Medvedev began Friday as the tournament's highest-ranked players following Novak Djokovic's shock exit, but both found themselves on the receiving end of comprehensive defeats.
World number three Tsitsipas was the victim as Fritz claimed his first victory over a top-10 ranked player on clay, ending the Greek's 12-match winning run at the competition with a 6-2 6-4 success.
Tsitsipas – who won the event in both 2021 and 2022 – was unable to contain Fritz as the American hit a series of huge winners en route to his third Masters 1000 semi-final.
Fritz will face Andrey Rublev in the final four after the fifth seed saw off the challenge of German qualifier Jan-Lennard Struff, posting a 6-1 7-6 (7-5) win.
Meanwhile, Medvedev came up short in his tussle with Rune, as the 19-year-old waltzed into his second Masters 1000 semi-final with a 6-3 6-4 triumph.
"It wasn't easy for sure, it's always tough to play Daniil," Rune said after his win. "It was actually my first time playing against him in a real match, but we've practised tonnes of times.
"I have huge respect for everything he's done. In the last week it was not easy to stop him, but I'm happy I managed to do it."
Rune now has a 10-8 record in meetings with his fellow top-10 players, and he will have to win another such duel to make the final, with Jannik Sinner his semi-final opponent.
Sinner needed 76 minutes to beat fellow Italian Lorenzo Musetti 6-2 6-2, and the 21-year-old now has the chance to reach his third Masters 1000 final, having previously finished as runner-up at two editions of the Miami Open.
On the same day fellow countryman Roger Federer would hang up his racquet at the Laver Cup, Wawrinka was forced to go all the way by his opponent in Metz, eventually winning 6-4 4-6 7-6 (7-5).
The three-time grand slam champion, whose injury struggles and form have seen him tumble to 284 in the world rankings, served up seven aces to Ymer's two, and made no double faults.
Victory moves him into the last four, where he will meet seventh seed Alexander Bublik after the Kazakh saw off Holger Rune in another three-set encounter with a 6-3 5-7 6-4 win.
Defending champion Hubert Hurkacz is also through to the semi-finals after making quick work of home favourite Arthur Rinderknech, winning 6-3 6-2.
The world number 10 will face Lorenzo Sonego next after the Italian also came through his quarter-final in straight sets against Sebastian Korda.
The 24-time major champion held his serve throughout a dominant Centre Court performance, triumphing 6-3 6-4 6-2 to move into the 60th grand slam quarter-final of his illustrious career.
Djokovic never looked troubled by his opponent, nor by the knee injury that required surgery last month, en route to setting up a last-eight meeting with ninth seed Alex de Minaur.
The seven-time Wimbledon champion dropped sets in his previous two victories but Rune's early showing suggested a routine victory from the off, as the Dane committed nine unforced errors in a one-sided first set.
Serbia's Djokovic latched onto those failures at will, taking just half an hour to seize a 1-0 match lead after breaking Rune's first service game and holding out from then on.
Rune improved in the second set, yet a cruel drop of service handed a 4-3 advantage to Djokovic, who then relinquished six set-point chances on his opponent's struggling serve.
A partisan crowd appeared in favour of Rune, celebrating every point won, yet Djokovic needed just one more set point to seal the second before glancing towards the spectators to quieten them down.
Djokovic repeated the dose in the third – and final – set, breaking Rune's opening serving game, though the 15th seed did squander an opportunity to break when attempting to level midway through.
That missed chance was once again punished emphatically as Djokovic secured another break in the following game before sealing a convincing victory in just over two hours.
Data Debrief: Djokovic edging toward Wimbledon history
Djokovic held a modest 3-3 against top-20 players in 2024 before this clash, though Rune proved no match for the Wimbledon veteran.
With this victory, Djokovic moved second in the all-time list for most quarter-final appearances at the grass-court major, surpassing Jimmy Connors (14) – only Roger Federer (18) can better the Serbian's 15.
Djokovic's next aim will be levelling Federer's record eight triumphs at Wimbledon, starting with a last-eight clash against De Minaur.
Djokovic came from a set down to beat Popyrin in four, confirming his place in the last 16 with a 3-6 6-3 6-4 7-6 (7-3) triumph. He will face Holger Rune next.
The world number two continued his record of having never lost to Popyrin in what was their third meeting, the previous one coming at the Australian Open earlier this year.
The Serbian praised Popyrin for his valiant effort, going on to admit the tie-break in the fourth saw him produce his highest level this year.
"It was another tough match. I didn’t expect anything less than what we experienced on the court today from Alexei," Djokovic said.
"I knew he was going to come to the match with confidence, a lot of self-belief. He was close to winning [when we played] in Australia earlier this year.
"With that serve and powerful forehand, he’s dangerous on any surface.
"I knew he was in form and he was going to come out believing he could win. He was the better player in the first set.
"I think I played a good second and third and the fourth was anybody’s game. He was serving very well. It was very difficult to read his serve.
"It was just a very challenging match, mentally as well, to hang in there. I'm not allowed to have big concentration lapses.
"I think I’ve done well in that regard in one of the best tie-breaks I’ve played this year, that’s for sure."
Data Debrief: Resilient Djokovic shows his class
While Djokovic was far from vintage in the first set, he showed the kind of resilience that we've seen throughout his career.
Djokovic became only the third player in the Open Era to achieve 50 Grand Slam match wins after turning 35, along with Ken Rosewall (64) and Roger Federer (62).
The 24-time grand slam champion breezed past Rune in straight sets on Monday, reaching his 15th quarter-final at the grass-court major, a tally only bettered by Roger Federer (18).
Denmark's Rune struggled throughout a humbling 6-3 6-4 6-2 defeat, though enjoyed the majority support at Wimbledon's top attraction, with Djokovic shushing the crowd at one point during the second set.
The seven-time Wimbledon winner noted that interaction in his on-court interview, hitting back at those who were against him.
"To all the fans that have had respect and stayed here tonight, I thank you from the bottom of my heart and I appreciate it," a visibly frustrated Djokovic said.
"And to all those people that have chosen to disrespect the player, in this case, me, have a good night!"
When Rishi Persad, master of ceremonies on Centre Court, suggested the support was purely for Rune and not to disrespect, Djokovic doubled down on his assessment.
"They were. They were. I am not accepting it. No, no, no, I know they were cheering for Rune but that's an excuse to also boo," the 37-year-old responded.
"Listen, I have been on the tour for more than 20 years. I know all the tricks. I focus on the respectful people that pay for the ticket, and love tennis and appreciate the players.
"I have played in much more hostile environments, trust me – you guys can't touch me."
Rune failed to break Djokovic's service throughout a one-sided clash as the latter set up a quarter-final meeting with ninth seed Alex de Minaur.
"I don't think he has played anywhere close to his best to be honest," Djokovic said of his 15th-seed opponent. "It was a tough start for him. He lost the first 12 points and I think that got to him mentally.
"Waiting all day to come out on the court is never easy. The tension is building up and [you are] stressed to get out on the court.
"On my end I think I've done things at the important moments. Things could have looked different if I lost those services games but very solid at the end and I'm very happy to get through in straight sets."
Djokovic appeared a doubt for this tournament, having pulled out of the French Open midway through at Roland-Garros before undergoing surgery for a troublesome knee issue.
"I'm feeling great on the court and let's take it day by day," Djokovic assured.
"There's always something to work on in the off days. I'll speak with my team tomorrow and analyse this match and get ready for the next one."
Last year's Paris Masters champion Rune, who is in the hunt for his first title of the season, beat the Frenchman 7-6 (7-2) 7-6 (7-5) and is yet to drop a set in the tournament.
The 19-year-old looks sharp, but so too does Jannik Sinner. Two years Rune's senior, the Italian made light work of his good friend and compatriot Lorenzo Sonego on Friday.
Sinner took just over 90 minutes to triumph 6-4 6-2 and tee up a semi-final with history-making 18-year-old Arthur Fils.
Fils, the world number 163, beat Quentin Halys to become the youngest Frenchman to reach a tour-level semi-final since Richard Gasquet in 2004.
"I have seen him [Fils] play here at this tournament," Sinner said of Fils, as quoted by the ATP Tour's official website.
"He is very strong physically already. He understands the game very well. He started off the year very well, so it is going to be an interesting match for sure."
Sinner will be the favourite despite Fils' hot streak, while Rune will go up against Maxime Cressy in a rematch of their Australian Open second-round match.
Cressy went down 7-5 6-4 6-4 in that meeting in Melbourne last month, though has the chance for revenge after seeing off Borna Coric 7-6 (7-2) 6-4.
