Meanwhile, two U.S. soldiers were wounded when an explosion destroyed their Humvee in the same Taliban stronghold, the latest evidence that militants are stepping up attacks ahead of Oct. 9 elections.
The rocket and small arms were fired at a Black Hawk helicopter on Monday in Zabul province, a military statement said.
No American troops were injured and there was no damage to the helicopter before another chopper — an Apache gunship — "engaged the enemy, killing six insurgents," the statement said. It did not elaborate.
The military said the two Americans were wounded on Monday in Shinkay, another district of Zabul close to the Pakistani border, when a homemade bomb hit their vehicle.
"The soldiers were out on a routine security patrol," the statement said. "One Humvee was destroyed."
It said the two wounded soldiers would be flown to Germany for treatment. It didn't identify the men or give details of their condition.
Zabul Gov. Khial Mohammed said the blast was caused by a freshly laid mine and blamed rebels from the former ruling Taliban for the attack. He said Afghan troops were scouring the area, but had found no suspects.
The military already reported the deaths on Monday of two American soldiers in a battle with insurgents in neighboring Paktika province, part of a tract of south and eastern Afghanistan where militants have led a stubborn insurgency since the Taliban were ousted in 2001.
The military also said Tuesday that three rockets were fired at a U.S. base in Paktika, but landed 50-100 meters (yards) away, injuring no one.
Another roadside bomb attack, this time on a convoy in the eastern city of Jalalabad, also caused no injuries, it said.
It was not clear when those two incidents took place.
President Hamid Karzai and one of his vice presidents have both escaped attacks in the past week, part of a wave of violence that officials predict will surge ahead of the country's first-ever direct presidential election.
Karzai is to address the U.N. General Assembly session in New York on Tuesday as his war-battered nation's interim leader. Most observers think he will win the vote handily against 17 opponents, many of them unknown to the majority of Afghans.
"If people can vote freely, I will win," Karzai said at a news conference this month.