KABUL—Seven U.S. troops, including three elite special-operations personnel, were killed along with three Afghan commandos and a translator Thursday morning when their helicopter crashed in Afghanistan's southern Kandahar province.

The Black Hawk helicopter crashed at about 10 a.m. in the Shah Wali Kot district in Kandahar, a hotbed of the insurgency, Afghan and Western officials said. A rescue team came under heavy fire when they approached the destroyed helicopter, coalition officials said.

"There...