It was the deadliest single incident in weeks for foreign troops in Afghanistan, where the radical Islamist Taliban movement has been waging a guerrilla war against the Afghan government and tens of thousands of NATO and U.S. troops.
ISAF said the cause of the crash was under investigation and gave no further details. A local official said the crash occurred around midday.
An ISAF statement said that four of the dead Americans were under ISAF command and the other three were part of a separate command known as U.S. Forces-Afghanistan, which often includes Special Operations forces. The statement also said that three members of the Afghan National Security Forces and an Afghan civilian translator died in the crash.
The United States has about 90,000 troops in Afghanistan, about half attached to ISAF and the rest under the distinct U.S. command.
A spokesman for the Taliban, Qari Mohammad Yousuf, said the militants shot down the helicopter, which he said had arrived in Shah Wali Kot as part of an operation against the insurgents.
“We have weapons that can hit aircraft,” he said by phone when asked to specify the type of weapon.
Maj. Martyn Crighton, an ISAF spokesman, said there were no reports of enemy activity on the ground at the time of the crash. He said it was too early to say what caused the crash.
Helicopters are a vital means of ferrying foreign troops and supplies in Afghanistan’s 11-year-old U.S.-led war.
Some of them go down because of bad weather or because of the rugged terrain, and some have been shot down by insurgents during combat.
The deadliest attack on foreign troops in Afghanistan occurred in August 2011, when insurgents shot down a U.S. CH-47 Chinook helicopter about 30 miles southwest of the capital, killing 30 American troops and eight Afghans.
The last crash of a Black Hawk in Afghanistan was on April 19, when four Americans were killed. Thursday’s death toll of seven Americans was the highest for a Black Hawk incident since the Afghan war began in 2001.
Julie Tate in Washington contributed to this report.