WASHINGTON, Aug. 1 — Former Defense Secretary Donald H. Rumsfeld said today he felt terrible about the military’s flawed handling of the death of Cpl. Pat Tillman, the former football star who was killed in Afghanistan. But he and other former Pentagon leaders insisted that there had been no attempt to cover up the way it happened.

Mr. Rumsfeld testified before a House committee that he felt “a great deal of heartbreak for the Tillman family,” not just because of the young soldier’s death but because weeks went by before the family learned that Corporal Tillman was killed by fire from his own side, rather than in a heroic fight with the enemy in Afghanistan, as the Army originally said.

“I do not recall when I first learned that Corporal Tillman’s death was fratricide,” Mr. Rumsfeld said, adding that it was probably after May 20, 2004, when he was told by a colonel about the possibility of a “friendly fire” incident.

Corporal Tillman, who turned down a lucrative National Football League contract to enlist in the Army after the terror attacks of Sept. 11, 2001, was killed on April 22, 2004.