Attahullah Khogyani, a spokesman for the provincial government, said the attack took place in the province's Achin district where Afghan and American forces have been fighting side-by-side against militants from the Taliban and the so-called "Islamic State".
The so-called "green-on-blue" attack is the latest in a line of incidents where Afghan soldiers have turned their weapons on global forces they are working with.
A U.S. warplane attacked a patrol of Afghan border police in the southern Helmand Province overnight, killing "several" and wounding a number of others.
"In (a) joint US-Afghan military operation". In Milwaukee, Pence commented on the shooting: "When heroes fall, Americans grieve".
Several American servicemen have been killed and injured after coming under fire in a "green-on-blue" attack in eastern Afghanistan, the Pentagon has announced. This could allow U.S. advisers to work with Afghan troops below the corps level, potentially putting them closer to fighting, a United States official said.
Some years ago, these green-on-blue insiderattacks on the global services were the major problem.
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Kazem, an Afghan army soldier, said that such attacks are sometimes planned by the Taliban, but most of the time it is caused by minor disagreements between the two sides.
Meanwhile, U.S forces in Afghanistan have released a statement and confirmed the death of Afghan border soldiers during overnight operations in Helmand.
"We will release more information when appropriate", a USA military spokesman said in a statement.
A US aircraft struck a checkpoint in the Helmand province during a joint operation.
The Pentagon apologized for the incident in a statement to BBC and said an investigation is underway.
The Taliban claimed responsibility in a statement by spokesperson Zabiullah Mujahid, who said a person loyal to the terror group infiltrated the Afghan army "just to attack foreign forces". "Our thoughts and prayers are with the families of American heroes". The Taliban said he was an infiltrator. American officials say the military has proposed sending an additional 2,000 to 4,000 US troops to Afghanistan, but the number may ultimately depend on how many additional troops are committed by North Atlantic Treaty Organisation partners.
The airstrike was part of an ongoing operation that was led by Afghan forces on the ground.