The fighting was taking place as NATO began an operation to recover the remains of the large transport helicopter that was shot down by insurgents early Saturday in the Tangi Joy Zarin area of Wardak province's Sayd Abad district, about 60 miles (97 kilometers) southwest of Kabul. The clashes Sunday did not appear to involve the troops around the crash site.
"There have been a small number of limited engagements in the same district as yesterday's helicopter crash, however those clashes have not been in the direct vicinity of the crash site," NATO said in a statement. "As of now, we have no reporting to indicate any coalition casualties resulting from these engagements."
Wardak provincial spokesman Shahidullah Shahid confirmed the helicopter recovery mission was under way and said there were reports of Taliban casualties overnight.
"There is a joint operation going on by Afghan and NATO forces.
A clearing operation is ongoing in the district and there are reports of casualties among insurgents," Shahid said. "The area is still surrounded by American forces."
Elsewhere in Afghanistan, NATO said insurgents killed four alliance service members in two separate attacks in the east and the south. It did not provide their nationalities or any other details.
The deaths bring to 369 the number of coalition troops killed this year in Afghanistan and 46 this month.
In an increasingly bloody conflict, the downing of the Chinook helicopter early Saturday marked the deadliest single loss for American forces in the decade-old war in Afghanistan.
Thirty American service members, an Afghan civilian interpreter and seven Afghan commandos were killed, the U.S.-led coalition said. A current U.S. official and a former U.S. official said the Americans included 22 Navy SEALs, three Air Force combat controllers and a dog handler, his dog and four crew members. The two spoke on condition of anonymity because military officials were still notifying the families of the dead.
Most of the SEALs belonged to the same elite unit that killed Osama bin Laden, although they were not the same people who participated in the May raid into Pakistan that killed the al-Qaida leader.
The downing was a stinging blow to the lauded, tight-knit SEAL Team 6, months after its crowning achievement. It was also a heavy setback for the U.S.-led coalition as it begins to draw down thousands of combat troops fighting what has become an increasingly costly and unpopular war.
Although there are thousands of special operations forces in Afghanistan, often taking part in dozens of night raids a month, their deployment in the raid in which the helicopter crashed would suggest that the target was a high-ranking insurgent figure. However, there has been no official word on the target of the raid.