Security forces had been tipped off about a gathering of militants in the eastern province of Paktika and raided their mountain ridge encampment in the early hours of the morning, they said.
The operation was targeted at the Taliban's radical Haqqani network that is linked to Al-Qaeda and said to be responsible for deadly attacks on both sides of the border, the US military said.
"In course of the operation 34 Taliban were killed," Paktika province government spokesman Hameedullah Zhohak told AFP.
Afghan police and US-led troops had first launched a ground attack on the group which had resisted and fought back for 15 minutes, Zhohak said.
"The troops called for air support and coalition helicopter gunships targeted the militant positions and killed all of them," Zhohak told AFP.
He said the militants left behind 27 motorbikes, four vehicles, more than 30 rocket-propelled grenades, machine-guns and automatic rifles.
The fighting was in Wor Mamay district which borders Pakistan's Baluchistan province and is near South Waziristan, both areas where extremist insurgents have bases.
Several of the militants at the camp detonated suicide vests they were wearing and grenades were rigged to explode as the security forces arrived, Julian said.
None of these explosions caused casualties to the Afghan and US forces, he said.
The clash comes after days of heavy fighting and increased attacks in Afghanistan with 34 people reported on Wednesday to have been killed in various incidents.
This included in the province of Logar, near the capital, where the US military said troops had killed four militants in a raid to capture an Haqqani commander.
The US government has offered five-million-dollar reward for the location, arrest or conviction Siraj Haqqani, said to be one of the most powerful commanders in the Taliban network.
He has reportedly admitted to an attack on a five-star hotel in Kabul in January 2008 and the attempted assassination of President Hamid Karzai at a military parade in the capital in April 2008.
US military officials have said he is trying to rival Mullah Mohammad Omar for the Taliban leadership.
"Haqqani has been a significant target because of their attacks on the population and the coalition forces," Julian told AFP.
"They have got activities on both sides of the border. We are looking for specific leaders out of that organisation and many of their fighters," he said.
Afghan and Western officials say militants are entering the battle in Afghanistan from Pakistan, which has in recent months stepped up pressure on extremists sanctuaries which have operated on its soil for years.
The militants are said to cross into Afghanistan to carry out attacks and withdraw across the border, where international soldiers are not allowed to operate.
Source: AFP South Asian Edition