According to reports, the Taliban members were killed in the Chikrinow district of the Panjshir province. The province has been the only region to hold out against the Taliban since the fall of Kabul on August 15.
The official Twitter account of the rebel group tweeted: “13 members of the Taliban were killed in an ambush by National resistance in the #Chikrinow district of #Panjshir province, and one of their tanks was destroyed.”
This latest ambush comes just 24 hours after eight Taliban fighters were killed after clashing with the opposition militia in the province.
Fahim Dashti, a spokesperson for the “National Resistance Forces (NRF)” said the fighting occurred on the western entrance to the valley where the Taliban attacked.
He said the attack, which may have been a test on the valley’s defences, was repulsed with eight Taliban killed and a similar number wounded.
Two members of the NRF forces were also wounded.
Massoud, son of the former anti-Soviet commander Ahmad Shah Massoud, established himself in the Panjshir valley with a force of several thousand.
It is made up of local militias and remnants of army and special forces units.
He has called for a negotiated settlement with the Taliban but said his forces would resist if their province in the narrow and mountainous valley is attacked.
The strike killed an individual, according to Navy Captain William Urban, who said there were no civilian casualties.
This came after US President Joe Biden authorised the strike following the devastating terrorist attack.
In a statement on Saturday, Mr Biden said: “The 13 service members that we lost were heroes who made the ultimate sacrifice in service of our highest American ideals and while saving the lives of others.
“Their bravery and selflessness has enabled more than 117,000 people at risk to reach safety thus far.
“May God protect our troops and all those standing watch in these dangerous days.”
Pentagon spokesman John Kirby echoed Mr Biden’s warning of “dangerous days” and said the threats are still very real.
He said on Saturday: “Threats are still very real, they’re very dynamic and we are monitoring them literally in real-time.
“And as I said yesterday, we’re taking all the means necessary to make sure we remain focused on that threat stream and doing what we can for force protection.
“They lost a planner and they lost a facilitator and got one wounded.
“The fact that two of these individuals are no longer walking on the face of the Earth, that’s a good thing.”