Kabul, Afghanistan (CNN) -- Coalition forces in Afghanistan have killed the Taliban insurgents responsible for the downing of a helicopter that left 38 U.S. and Afghan personnel dead, the commander of U.S. forces there and NATO announced Wednesday.

A precision airstrike killed Mullah Mohibullah -- a Taliban leader -- and the insurgent who fired what's believed to be the rocket-propelled grenade that brought down the helicopter, according to Gen. John Allen, the commander of U.S. forces in Afghanistan. Several of their Taliban associates were also killed, NATO's International Security Assistance Force said.

"This does not ease our loss, but we must and we will continue to relentlessly pursue the enemy," Allen told Pentagon reporters assembled for a video news conference Wednesday.

The strike took place in Chak district, Wardak province, on Monday, the ISAF said.

A Taliban spokesman could not be immediately reached for comment. Wardak provincial spokesman Shahidullah Shahid also could not be reached for comment.

The attack on the helicopter Saturday represented the worst single-incident loss of American life since the start of the Afghan war. Thirty Americans died in the crash, military officials said. The other victims were Afghan personnel.

The Pentagon will put the Navy SEAL death toll in the helicopter downing at 17, according to two Defense Department officials. Originally, Pentagon sources told the news media that 22 SEALs were killed.

Mohibullah was a key facilitator in an insurgent attack cell led by Din Mohammad, a Taliban leader killed in a previous Special Operations mission, Allen said. Mohibullah had as many as 12 Taliban fighters under his command, including potential suicide bombers.

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

ISAF troops found and followed the two into a wooded area and, after ensuring no civilians were around, called for the airstrike, the statement said.

Allen said the aircraft involved in the strike announced by NATO was the F-16, but he didn't say how many.

Allen said the strike didn't kill the Taliban leader that U.S. forces were hunting the night of the fatal attack, but he confirmed that Mohibullah was killed in the F-16 strike announced Wednesday.

The remains of all 38 of those killed in Saturday's incident arrived at Dover Air Force Base in Delaware on Tuesday for a "dignified transfer." Because the catastrophic nature of the crash made the remains difficult to identify, all were brought to the United States.

The Air Force Mortuary Affairs Office explained that a "dignified transfer" is not a ceremony, but rather "the process by which, upon the return from the theater of operations to the United States, the remains of fallen military members are transferred from the aircraft to a waiting vehicle and then to the port mortuary."

Pentagon spokesman Col. David Lapan said the names, ages, hometowns and military units of the slain Americans will be released within the next 24 hours. He said the public announcement has been delayed for security reasons.

The Afghan remains will be returned to their families once identifications can be made, U.S. officials said.

CNN's Joe Sterling, Larry Shaughnessy, Barbara Starr and David Ariosto contributed to this report