Bill Belichick described Don Shula as "the standard for consistency and leadership in the NFL" following the Miami Dolphins legend's death at the age of 90.
Shula, whose passing was announced by the Dolphins on Monday, is the NFL's all-time leader for wins by a head coach.
He won 347 games in a remarkable career that saw him lead Miami to the only perfect season in NFL history in the 1972 campaign.
Shula oversaw a successful defence of that Super Bowl title and guided the Dolphins to two further appearances in the showpiece during 26 seasons with Miami.
New England Patriots coach Belichick has six Super Bowl rings as a head coach and is closing in on Shula's record, having claimed 304 victories in his career.
Belichick grew up in Maryland as his father was an assistant coach at the Naval Academy in Annapolis when Shula was a head coach with the Baltimore Colts, with whom he won an NFL title in 1968.
Paying tribute to Shula, Belichick said in a statement: "Don Shula is one of the all-time great coaching figures and the standard for consistency and leadership in the NFL.
"I was fortunate to grow up in Maryland as a fan of the Baltimore Colts who, under coach Shula, were one of the outstanding teams of that era.
"My first connection to coach Shula was through my father, whose friendship with coach Shula went back to their days in northeast Ohio.
"I extend my deepest condolences to the Shula family and the Dolphins organisation."
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