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 told AFP, "Our mujahideen shot down an Isaf helicopter in Chenarto area of Shah Wali Kot district in Kandahar province at around 11:00 am (0630 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 told AFP.
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.
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.
On March 16, a Turkish helicopter crashed into a house on the outskirts of Kabul, killing 12 Turkish soldiers and two Afghan civilians.
The deaths of the seven Americans come just a week after six others were killed by their local Afghan colleagues in so-called green-on-blue attacks, eroding trust between foreign troops and the Afghans they work with.
Nato's International Security Assistance Force said last month that attacks in the second quarter of this year were 11 percent higher than in the same period last year.
The month of June alone saw the highest number of attacks in nearly two years, with more than 100 assaults a day across the country, including firefights and roadside bombings, the US-led coalition said.
Civilians continue to bear the brunt of the war, with more than 40 killed on Tuesday in a series of suicide attacks and homemade bomb blasts across the country in the bloodiest day for ordinary Afghans this year.
Nato troops fighting the insurgency by Taliban militants are scheduled to leave Afghanistan gradually and hand over responsibility for national security to Afghan forces by the end of 2014.
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there is no point fighting here or there(af-pak). america-pak-afghan govt should decide to talk to taliban and come to reconciliation. even if that means giving them safe heavens like fata and south afghanistan.