The four Afghans included three members of the security forces and a civilian interpreter, NATO’s US-led International Security Assistance Force (ISAF) said.
“The cause of the crash is under investigation,” it said, adding that the helicopter was a UH-60 Black Hawk. The statement gave no further details.
Taliban spokesman Qari Yusuf Ahmadi said: “Our mujahideen (holy warriors) shot down an ISAF helicopter in Chenarto area of Shah Wali Kot district in Kandahar province at around 11:00 am (06:30 am GMT).”
He said a rocket-propelled grenade had been used against the helicopter.
“The helicopter was destroyed and all the crew and soldiers inside were killed,” Ahmadi said.
“The NATO helicopter was hit by a Taliban rocket in Khashir area of Chenarto village in Shah Wali Kot district this morning,” a local official who requested anonymity said.
The area had been cleared of Taliban in a push by NATO and Afghan forces in 2010, but the insurgents had become active in the district again, district governor Obaidullah said.
“Taliban have been active in Chenarto village since the beginning of this year. Afghan and foreign forces have had frequent clashes with the Taliban in this district since the beginning of this year,” said Obaidullah, who uses just one name.
The ISAF statement did not use its normal phrasing for a simple helicopter crash, which includes the line that no enemy activity was reported in the area.
Helicopter crashes are fairly frequent in Afghanistan, where the 130,000-strong NATO mission relies heavily on air transport.
Read more: Al Jazeera