Italian Football Federation (FIGC) president Gabriele Gravina says not finishing the season would lead to a "series of disputes" and he already has "warnings on his table" from clubs.
Serie A was suspended indefinitely in March, after some matches were played behind closed doors, due to the coronavirus pandemic.
The FIGC said the top flight will not begin again until the health and safety of those involved can be guaranteed and an extension by the Italian government on strict restrictions on movement and outdoor activities until May 3 makes a swift resumption unlikely.
Reports in Italy have suggested some clubs are keen to return to training at that time and resume playing by the end of May.
Gravina reiterated his stance that the campaign must be finished in full, especially given reports FIFA has agreed to extend 2019-20 indefinitely to allow domestic leagues time to complete the season.
"A definite stop would start a series of disputes. There are already some warnings from some clubs on my table," he told La Repubblica.
"FIFA has paved the way. The new season will not begin without having concluded the first. We don't have a deadline to start again; we will go hand in hand with the other European Leagues.
"If they let us play in early June, we have the dates to end at the end of July."
Gravina added that for now the plan is working out the logistics for how football can resume in Italy.
"I respect science, but I can't give up. We work on how to get back to playing, not on when," he added.
"When Italy comes back to life and when there will be the right conditions for other sectors to resume, football will also return.
"I say it once and for all: the championship must be completed. There's time. The government, league, FIGC, doctors – we will all decide together responsibly.
"Our entire system would benefit from us restarting."
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