German Brig. Gen. Gunter Katz, a spokesman for the U.S.-led coalition, disclosed their nationalities at a briefing, but said he could not provide other details about the incident because it was still under investigation. He said a seventh NATO service member killed Sunday in a separate insurgent attack in the south also was an American.
The Taliban on Monday claimed responsibility for the deaths of the six U.S. troops - the latest caused by bombs planted by insurgents along roads, paths or mountain tracks.
Taliban spokesman Zabiullah Mujahid said in a statement the blast struck the U.S. troops in their armored vehicle around 8 p.m. Sunday in Wardak province, just south of Kabul.
Coalition and Afghan forces are trying to secure areas of Wardak that insurgents use as gateway into the Afghan capital where they stage high-profile attacks on Afghan government and NATO targets.
Wardak provincial police chief Gen. Abdul Qayum Baqizoi said that after the explosion in Jalrez district, a coalition airstrike killed a local Taliban commander and wounded three insurgents.
Also in the east, authorities said gunmen assassinated a chief prosecutor in Ghazni province Monday morning as he drove to work. Mohammad Ali Ahmadi, the deputy provincial governor, said Sahar Gul was shot twice - once in the head and once in the chest.
The Taliban routinely target Afghan government officials to weaken support for President Hamid Karzai's administration.
In the south, three suicide bombers riding in a three-wheeled vehicle blew themselves up Monday afternoon in Kandahar city, killing two children and wounding six other civilians, said Kandahar provincial spokesman Ahmad Jawed Faisal. He said authorities had not determined the target of the explosion.
A surge in Afghan and coalition forces during the past two years has routed Taliban fighters from many of their strongholds in the south, but the insurgents have stepped up their attacks this summer to take back key areas.
Separately, President Hamid Karzai on Monday condemned the public killing of a married Afghan woman who was accused of allegedly running off with another man.
In a statement, Karzai called the execution-style slaying an unforgiveable crime. A video of the killing, which surfaced recently, showed the woman being shot multiple times as people stood nearby cheering.
Before it collapsed in 2001, the hardline Taliban regime carried out public executions of women, mostly for adultery.
Police in Shinwari district of Parwan province say the Taliban were behind the woman's slaying, which occurred about up to 12 days ago.
Karzai's condemnation comes as donor nations met in Tokyo to pledge $16 billion in aid for Afghanistan. The donors expressed strong concerns over how the money will be handled and also called on Kabul to improve human rights, especially women's rights.
"Such a crime is unforgivable in the sacred religion of Islam and the laws of the country," Karzai said.
The U.S. Embassy in Kabul and the top commander of U.S. and NATO forces on Sunday also condemned the killing of the woman.