KABUL, Afghanistan — Two NATO service members were killed in Afghanistan on Monday after coming under fire by enemy forces in separate incidents, officials with the U.S.-led military coalition said.

The International Security Assistance Force, as the coalition is known, didn't immediately provide details or the nationalities of the soldiers who were killed. Officials said only that one of the fatal incidents occurred in eastern Afghanistan and the other in the south.

Sarhadi Zowak, a spokesman for the governor of eastern Afghanistan's Laghman province, confirmed that Afghan forces were carrying out a military operation in the district of Alingar, but he could not confirm the causality.

"Afghan forces have launched a military operation … but there are no further details about the circumstances of the operation," Zowak said, citing poor cellphone service in the area.

In a statement, the Taliban claimed responsibility for killing two U.S. soldiers during an attack in the area, but the insurgent group regularly exaggerates battlefield reports.

"Early this morning, the American soldiers wanted to attack the mujahedin," or holy warriors, the statement said. "They faced heavy ambushes by the mujahedin. As a result, two American soldiers were killed."

Local officials in southern Afghanistan said they had no information about a coalition fatality in that part of the country.

Although U.S. and coalition forces are withdrawing troops from Afghanistan, the Taliban-led insurgents continue to launch attacks in a bid to regain territory.

Monday's incidents came nearly a week after six U.S. soldiers were killed when their aircraft crashed in Zabol province, in the south, bringing to 10 the total number of coalition fatalities so far this month.

Baktash is a special correspondent. Times staff writer Shashank Bengali in Washington contributed to this report.