The commander, Gen. John R. Allen of the Marines, said the military in Afghanistan had tracked the insurgents after they shot down the helicopter on Saturday, most likely with a rocket-propelled grenade.

A group of insurgents, numbering fewer than 10, were together as the location was hit by an F-16 strike, General Allen said. The airstrike occurred Monday, Pentagon officials said.

In a video briefing to the Pentagon from his headquarters in Kabul, General Allen said the Chinook helicopter on a weekend mission also took small arms fire as it entered the Tangi Valley in Wardak Province, just west of Kabul; an investigation has been started to determine the exact cause of the crash.

Those killed included 22 members of the elite Navy Seals; three Air Force special operations personnel; an Army helicopter crew of five; seven Afghan commandos; and a civilian Afghan translator. It was the greatest loss of American life in a single day in the almost 10 years of the war.

The Chinook was called to the scene of a firefight in which Army Rangers were trying to capture or kill a local Taliban leader responsible for a series of attacks, including the planting of improvised roadside bombs.

General Allen said the Taliban leader who was the target of the original mission still eludes American and allied forces; he declined to identify the Taliban leader. “We will continue to pursue that network,” he said.

The follow-up mission that killed the militants “does not ease our loss,” General Allen said.

While acknowledging that there are “challenges ahead” to the American-led mission in Afghanistan, General Allen described the shooting down of the helicopter as a single, tragic episode in a much broader campaign.

A press statement released by the military headquarters in Kabul said the airstrike killed a Taliban leader named Mullah Mohibullah, who was part of the group that shot down the helicopter and subsequently escaped.

“After an exhaustive manhunt, Special Operations forces located Mullah Mohibullah and the shooter after receiving multiple intelligence leads and tips from local citizens,” the statement said. “The two men were attempting to flee the country in order to avoid capture.”

The statement said that security forces “located and followed the insurgents to a wooded area in Chak district. After ensuring no civilians were in the area, the force called for the airstrike which resulted in the deaths of the Mullah Mohibullah, the gunman, and several of their Taliban associates.”