The attack occurs as the Trump administration accelerates efforts to foster a peace deal with the Taliban, which remains a potent threat nearly 18 years after USA forces entered Afghanistan in the wake of the September 11, 2001, attacks.
The Taliban have held talks with a USA envoy in recent months while continuing to carry out daily attacks on Afghan forces.
Two Americans, an Army Green Beret and explosive ordnance disposal (EOD) specialist, were killed during a mission in Kunduz province last month.
Three other Americans service members were also wounded in the attack, which occurred near Bagram Air Base. "The contractor, an Afghan citizen, was initially treated along with other injured civilians, later identified as a contractor and treated at Bagram Airfield".
A government counteroffensive has since regularly carried out air raids against Taliban positions in the district and USA -led coalition planes have assisted, the Defense Ministry in Kabul said Monday.
The deadly assault comes as the Trump administration negotiates with the Taliban for a permanent peace deal in Afghanistan, where USA troops have operated since late 2001 in what is now the longest military engagement in American history.
The names of the service members killed in action were being withheld until 24 hours after notification of next of kin, in accordance with U.S. Department of Defense policy.
Earlier three people were killed in twin explosions in the eastern city of Jalalabad.
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Qari Yusouf Ahmadi, a Taliban spokesman, claimed responsibility for the attack and said the group's fighters also seized weapons and ammunition. The conflicting accounts could not be immediately reconciled.
An official from the provincial governor's office, who was not authorized to speak with the media, confirmed the attack and said there were casualties among the Afghan forces, but couldn't provide exact figures.
Four were passers-by and the fifth was a driver of a vehicle going down the road, said Abdul Raqib Kohistani, the Bagram district police chief.
While their primary mission is to advise and assist Afghan security forces, USA troops continue to conduct daily patrols throughout Afghanistan.
Last year, 13 USA service members were killed in Afghanistan.
The Taliban have continued to carry out daily attacks on Afghan security forces despite holding several rounds of peace talks with the United States in recent months. The Taliban have refused to meet with the Afghan government, which they view as a US puppet.
The deaths bring the number of American troops killed in Afghanistan this year to seven.
Abdullah said the Taliban could partake in elections and even compete for the presidency if they renounce violence.