A total of 20 people, including two foreign soldiers, were also killed in earlier clashes in the country.
The fighters were killed in eastern mountains near the Pakistani border, said Akram Khelwak, the Paktika provincial governor.
One Afghan police officer was wounded in the assault, in which helicopter gunships and artillery fire supported troops on the ground, he added.
The operation comes as Nato prepares to launch the largest military offensive in Afghanistan since the fall of the Taliban regime in 2001.
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 are going to go into these areas, take out the security threat and establish conditions where... humanitarian organisations can begin the real work that needs to be done"
Colonel Tom Collins, US military spokesman
"We believe 12 suspected Taliban were killed in the bombing," Innes said.
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.
Four people also died when a rocket, fired by suspected Taliban fighters, hit their home in Paktika, local authorities said.
The Nato offensive, dubbed operation Mountain Thrust, is due to begin on Thursday and will involve up to 11,000 US, British, Canadian and Afghan troops.
It is aimed at driving Taliban fighters from the country's volatile southern provinces - Kandahar, Helmand, Zabul and Uruzgan.
Forces will be deployed in
Afghanistan's Helmand province
"This is not just about killing or capturing extremists," said Colonel Tom Collins, a US military spokesman, on Wednesday.
"We are going to go into these areas, take out the security threat and establish conditions where government forces, government institutions, humanitarian organisations can move into these areas and begin the real work that needs to be done."
The offensive coincides with a surge in Taliban attacks in Afghanistan's southern and eastern provinces near the Pakistani border, where Afghan authorities exert little control.