In a statement sent to VOA, Mujahid said American forces were engaged in a meeting with members of a pro-government Afghan militia when two Taliban infiltrators opened fire on them.
Details are still not entirely clear on what happened, but the United States troops were in an "active ground engagement" in the Achin District of Nangarhar, an area that has one of the biggest numbers of ISIS fighters in Afghanistan.
Gresback said they were investigating the incident.
It said 10 insurgents were killed but denied reports from local sources saying that American soldiers were among the dead.
The U.S. military says a U.S. and Afghan team was lured to a meeting by insurgents posing as friendly militia members in eastern Afghanistan, triggering a shootout and a coalition airstrike on the compound.
While some Afghan officials said at least two USA soldiers were killed in what was described as an insider attack by friendly forces, Capt. Tom Gresback, a US military spokesman in Afghanistan, said only one US service member had been wounded.
Western officials say most insider attacks stem from personal grudges and cultural misunderstandings rather than insurgent plots.
While Afghan security forces are conducting most of the fighting against IS and Taliban militants, United States troops operate alongside them in a training capacity and are frequently on the front lines.
The attack came hours after the provincial government announced in a statement that Afghan forces killed almost two dozen Taliban insurgents, including four commanders, in the nearby Khogyani district. Afghan forces backed by US air power routinely conduct anti-terrorism operations in the province bordering Pakistan. Eight U.S. service members have been killed in the province over the past nine months.