Major Quentin Innes, a spokesman for international forces in southern Afghanistan, said on Wednesday that a US soldier had died in an ambush in the southern province of Helmand on Tuesday.
The ambush caused a clash in which coalition forces backed by helicopters and planes attacked Taliban positions.
"We believe 12 suspected Taliban were killed in the bombing," Innes said, adding that the coalition was assessing if there were any civilian casualties in the air strikes.
The US military said another foreign soldier was killed in eastern Kunar province on Tuesday but did not give his identity.
Two Taliban fighters were killed in a gun battle in the province of Zabul after they ambushed a US convoy, wounding two American soldiers.
Taliban officials could not be immediately contacted.
The upsurge in fighting comes as Nato forces prepare to take over from US troops in the Taliban heartland in the south.
Almost 40 foreign soldiers have been killed in combat in Afghanistan this year, nearly 30 of them Americans.
They are among more than 900 people killed this year, more than 400 in May.
The increase in fighting is the bloodiest since coalition forces backed by Afghan factions overthrew the Taliban government after its leadership refused to hand over al-Qaeda leader Osama bin Laden in 2001.
The coalition forces also announced on Wednesday that their biggest campaign since 2001 had been launched in the middle of May and was still under way.
The campaign involves 11,000 troops from Britain, Canada and the United States, as well as Afghan soldiers.