JALALABAD, Afghanistan — The American military bombed members of an Afghan government militia who were on the front lines of the battle against the Islamic State in eastern Afghanistan, killing at least 13 fighters after at least one opened fire on American Special Forces soldiers deployed there, Afghan officials said Thursday.

While some Afghan officials said that at least two American soldiers were killed in what was described as an insider attack by friendly forces, Capt. Tom Gresback, a spokesman for the United States military in Afghanistan, rejected those reports and said that only one American service member had been wounded.

Captain Gresback would not say whether the service member had been wounded by friendly fire, or whether the United States had bombed the militia afterward.

The episode unfolded in the Achin district of Nangarhar Province, the stronghold of the Islamic State’s affiliate in Afghanistan. Over the past year, Afghan forces, with the help of American Special Forces units and airpower, have tried to wipe out the group there, but it has been an uphill task because the Afghan government has had little control in the area for many years. Every time the Islamic State has been squeezed in Achin, the fighters have shifted to a neighboring district.