Police sent to the area where the helicopter came down Sunday, in a rugged rural area of Logar province south of Kabul, had a firefight with the militants but pulled back for lack of support, the Logar police chief said.
The Taliban claimed the 11 were US military personnel. After the helicopter came down in bad weather, they "were captured alive and were then transferred to the most secure region of the nation", the militants said in a statement.
The US-led International Security Assistance Force (Isaf) said no foreign military were involved and the helicopter was a civilian one.
Turkey's foreign ministry said eight of its nationals were seized and its diplomats were holding "intensive talks" with Afghan authorities to trace their whereabouts.
"We hope that our nationals will be rescued as soon as possible and safely returned to the regions where they work," Turkish Deputy Prime Minister Bulent Arinc told reporters.
Russia's foreign ministry said two pilots - a Russian named Pavel Petrenko and a Kyrgyz national who was not identified - were among those captured. An Afghan was also detained.
The Afghan-based charter firm Khorasan Cargo Airlines, which operated the MI-8 helicopter, said the Turks were working on a road project.
The Afghan interior ministry said a police team had been sent to the area and a search for the passengers and crew had begun. It could not confirm the number or nationality of those held.
"Police were sent to the area where the helicopter made an emergency landing and engaged in a firefight with the Taliban," Abdul Saboor Nasrati, Logar provincial police chief, told AFP.
"We pulled the police back because there was no help from the Afghan army or foreign forces. The police were unable to secure the area, which is very rural, and we were worried," Nasrati said.
Hamidullah Hamid, governor of Azra district near where the helicopter came down, said the detained Afghan was acting as an interpreter.
Isaf is preparing to withdraw all its foreign combat troops from Afghanistan by the end of 2014, handing over to Afghan troops and police despite widespread fears about instability in the country.
An Isaf spokesman said Nato troops were ready to assist Afghan security forces but there had been no request so far.
A Logar provincial government spokesman, Din Mohammad Darvish, said provincial officials have been talking to village elders to try to persuade the Taliban to release the captives.
The helicopter had been travelling from the eastern city of Khost to Kabul when it was forced to land.
The Taliban, ousted from power in 2001 by a US-led invasion, claimed it had 11 US military members, including two translators, on board.
"The foreign forces, by disassociating themselves from the helicopter, are trying to make it seem as the detainees are civilians but denial will not benefit them as all were captured while wearing American military uniforms," it said.
Attacks by the Taliban and other guerrillas soared in the first quarter of 2013, according to a study by an independent group released on Saturday.
The Afghanistan NGO Safety Office reported 2,331 insurgent attacks in January-March, a 47 percent rise on the first quarter of last year.
Helicopter mishaps are common in mountainous Afghanistan.
Last month five foreign soldiers died in a crash in the south of the country. In February this year a Nato helicopter came down in the east but there were no fatalities.
Turkey, one of only two Muslim-majority members of Nato, has around 1,800 soldiers serving with ISAF. But unlike its European allies, their mission is limited to patrols and its troops do not take part in combat operations.
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