WASHINGTON — Georgetown parted ways Thursday with John Thompson III, its men’s basketball coach for the past 13 seasons, in a painful separation from a family coaching tradition that built a national power in the 1980s and guided the program for more than four decades.

Thompson, 51, led Georgetown to eight NCAA tournament appearances, including a run to the Final Four in 2007, since taking over in 2004. The program had faltered in recent seasons, however, finishing the past two with losing records and missing out on the NCAA tournament for three of the past four.

Students, alumni and others within the fan base had called for Thompson’s dismissal from the program, which had not compiled consecutive losing seasons since 1971-72 and 1972-73. The latter season was the program’s first under Thompson’s father, Hall of Fame coach John Thompson Jr., who transformed the Hoyas into a college basketball icon over more than 26 seasons.

“It is with profound regret and deep appreciation that I informed John Thompson III this morning that the university will no longer be retaining his services as head men’s basketball coach,” Georgetown president Jack DeGioia said in the statement. “Our tradition of excellence will forever be inextricably linked with John and his family.”

The decision was particularly uncomfortable for DeGioia given his long-standing friendship with Thompson Jr., who directed Georgetown to the 1984 national championship as part of three Final Four berths over four seasons.

Thompson Jr., 75, remains a towering figure on campus, a sideline presence at nearly every Hoyas home game. He maintains an office on campus at the John Thompson Jr. Intercollegiate Athletic Center, a 144,000-square foot athletic facility that opened last year at a cost of approximately $62 million.

Thompson III had been one of two active coaches in the Big East to appear in the Final Four, but since then Georgetown has not advanced out of the first weekend of the NCAA tournament.