The bodies of two women were recovered from the rubble after the crash in Bagrami district, in the east of the capital, the local interior ministry told AFP, correcting an earlier death toll.
Police and local residents were digging to find survivors, ministry spokesman Sediq Sediqqi told AFP.
The Turkish military said 12 of its soldiers were killed when the Sikorsky helicopter came down at 10:25 am (0555 GMT), in what is believed to have been the deadliest incident for its troops in Afghanistan.
A spokesman for the US-led NATO force in Kabul confirmed the helicopter was operated by the International Security Assistance Force.
"We are investigating the cause of the crash but there were no reports of insurgent activity in the area," he said.
Kabul CID chief Mohammad Zaher said the final death toll was "12 Turkish nationals onboard the chopper plus two Afghan civilians living in the residential house".
The Afghan interior ministry said a boy was also wounded.
The civilian casualties were likely to be another source of upset for Afghan leader Hamid Karzai who on Thursday called on international troops to stop patrolling in villages after an American soldier killed 16 civilians on Sunday.
Turkey, NATO's sole Muslim member, currently has around 1,800 soldiers serving in the US-led International Security Assistance Force (ISAF) in Afghanistan, deployed in Kabul, neighbouring province Wardak in the north.
In October, Turkey extended by another year its Kabul regional command of the ISAF. Unlike its European allies, Turkey's mission is limited to patrols and its troops do not take part in combat operations.
Turkey refused a combat role against Islamist insurgents in a country where it has historically close ties with Afghans.
Helicopter crashes are fairly frequent in Afghanistan, where poor roads mean that the 130,000-strong NATO mission relies heavily on air travel.
Last August, an American Chinook was shot down by the Taliban near Kabul, killing eight Afghans and 30 Americans, including 22 Navy SEALs from the same unit that killed Osama bin Laden in neighbouring Pakistan earlier that year.
It was the deadliest single incident for American troops in 10 years of war in Afghanistan.
NATO combat troops are scheduled to leave Afghanistan gradually and hand over responsibility for national security to Afghan forces by the end of 2014.
On Thursday, Karzai said his government would be ready to take over in 2013.
Copyright AFP (Agence France-Presse), 2012