In the western Farah province, Afghan and foreign soldiers bombed a Taliban hideout where two hostages were being held, killing eight fighters, Jalander Shah, an Afghan army commander, said.
Both hostages were freed during Friday's operation, he said.
In yet another incident, the US-led force and Afghan troops battled Taliban fighters, then called in air strikes, in the eastern Khost province.
Two Taliban fighters were killed and four others detained during the operation in the Sabari district, the US-led force said in a statement.
The clash took place during a raid on a compound suspected of housing Taliban fighters involved in bomb-making activities.
The joint force searched several compounds and recovered weapons and ammunition, it said.
More than 1,200 people have died in clashes between the multinational force and Afghan troops so far this year, according to results compiled by the Associated Press news agency.
New prison planned
In other news from Afghanistan, the New York Times reported on Saturday that the US intends to build a "big new prison" in the country.
The Pentagon is moving forward with plans to build a 40-acre detention complex on the main American military base in Bagram, the daily quoted officials as saying.
They conceded that even the new prison will not be able to absorb all the Afghans currently being detained by the US, or the influx of new prisoners from the escalating fight against al-Qaeda and the Taliban.
The proposal comes at a time when Bush administration officials continue to stress that they want to close down the US-run prison camp at Guantanamo Bay in Cuba.
Classrooms will be built for vocational training and religious discussion, and there will be more space for recreation and family visits, officials said.