The Taliban fighters responsible for downing a helicopter packed with Navy SEALs and other troops were killed in a series of airstrikes Monday, U.S. military officials said, although the original target of the commandos’ mission remained at large.

A group of “less than 10” insurgents, including the fighter who allegedly shot the Chinook helicopter with a rocket-propelled grenade, were tracked down at a compound in eastern Afghanistan early Monday and killed in airstrikes by F-16 fighter planes, according to Marine Gen. John R. Allen, the top commander in Afghanistan, and other military officials.

Allen and other officials would not say how they were able to determine which Taliban fighter fired the deadly shot but said they were able to track down the insurgents after “receiving multiple intelligence leads and tips from local citizens,” according to a military statement released in Kabul. The statement said that the unnamed shooter was attempting to flee the country when he was found in Wardak province.

In a news conference Wednesday with Pentagon reporters conducted by video link, Allen declined to answer most questions about Saturday’s helicopter crash, which took the lives of 30 U.S. troops, seven Afghan soldiers and an Afghan interpreter — the deadliest single incident for U.S. forces in the decade-long war. The incident is now under investigation.

Initial reports suggested that the Chinook was dispatched to rescue a unit of Army Rangers engaged in a firefight with insurgents in a remote part of the Tangi Valley in Wardak province. But Allen said the commandos were sent primarily to chase after some insurgent leaders who had gotten away from the Rangers.

“The purpose of this mission was to go after the leadership of that network,” he said. Although the Rangers did kill some Taliban fighters, “there were elements that were escaping,” Allen said. The commandos were trying “to contain that element from getting out.”

The original target of Saturday’s manhunt eluded capture and remains on the loose, Allen said. He declined to name the insurgent leader.

The Chinook crash was the latest in a string of setbacks in the war effort, after the assassination of two key Afghan government officials in Kandahar last month and a brazen Taliban attack on the Intercontinental Hotel in Kabul in late June.

But in his first news conference since taking command of U.S. and NATO forces in Afghanistan, Allen said the allies’ strategy was working and described the Taliban as a weakened force.

“All across Afghanistan, the insurgents are losing. They’re losing territory, they’re losing leadership, they’re losing weapons and supplies, they’re losing public support,” he said. “More and more, the insurgents are losing resolve and the will to fight.”

Also Wednesday, the Pentagon for the first time said it would release the names of the U.S. troops killed in the Chinook crash but acknowledged that some senior military commanders had lobbied to keep the identities a secret.

Officials from the U.S. Special Operations Command had asked Defense Secretary Leon E. Panetta to not publicly identify most of the troops.

Panetta considered the request but decided to order the disclosure of the troops’ names, rank, age, unit and home town in keeping with past practice, said Marine Col. Dave Lapan, a Pentagon spokesman. Lapan said Wednesday morning that the information would be released “within 24 hours.”

Withholding the names would have represented a break from the Pentagon’s longtime policy of identifying every service member killed in the line of duty. Most of the names had been revealed in recent days by grieving relatives and friends in interviews with reporters.