A battle in western Afghanistan that included airstrikes killed dozens of Taliban militants after an insurgent ambush left three U.S. troops dead, an Afghan official said Sunday.

The hours-long battle took place Saturday in the western province of Farah after a complex attack that killed three Americans and seven Afghan troops, said Afghan army spokesman Maj. Abdul Basir Ghori.

The insurgent ambush involved two roadside bombs, gunfire and rocket-propelled grenades, Capt. Elizabeth Mathias, a U.S. military spokeswoman, said Sunday. Mathias confirmed that fighting in the west continued for six to eight hours after the ambush, but she could not provide any casualty figures.

"The combined ISAF and Afghan force was receiving significant small-arms, RPG and indirect fire throughout that time frame," she said, referring to the NATO-led International Security Assistance Force.

Ghori said about 50 militants were killed in Saturday's battle, but no other Afghan officials could immediately confirm that figure.

NATO aircraft bombed areas where militants were firing from, Mathias said.

"We are not sure right now how many people those munitions killed," she said.

During the clash, a rocket fired by militants hit a home and killed a woman and a teenage girl, said Afghan police spokesman Raouf Ahmadi.

The fighting took place in the Bala Baluk district of Farah province, a region controlled by militants that has been the site of huge battles in the past, some that have caused high numbers of civilian casualties.

Saturday's violence came the same day Afghan officials said 50 civilians, security forces and militants were killed in a spate of attacks around Afghanistan, including 20 noncombatants killed in two roadside bomb explosions.

Violence has risen steadily across Afghanistan the last three years, and militants now control wide swaths of the countryside. The U.S. and NATO have a record number of troops in the country, and the top commander in Afghanistan, Gen. Stanley McChrystal, is soon likely to request thousands more.

Support for the eight-year war is waning in the United States and Europe as troop deaths rise and Taliban attacks spike. A record number of U.S. and NATO troops have died in Afghanistan already this year.