The Taliban on Thursday said they had captured the center of Shutul district in Panjshir along with 11 outposts held by opposition forces.
A member of the Taliban's cultural commission said that 34 members of the opposition forces were killed in the ongoing clashes that began last night.
The Taliban shared a video online saying their forces had advanced in Shutul district.
"A heavy toll has been inflicted on the opposite side in last night's operations as well as in this morning's clashes in Shutul district of Panjshir," said Inamullah Samangani, a member of the Taliban's cultural commission.
However, forces loyal to Ahmad Massoud rejected the figures and claimed that the Taliban has suffered heavy casualties.
A spokesman for the opposition front, Fahim Dashti, said 350 Taliban fighters were killed and at least 290 more were wounded in the clashes in the last four days. The Taliban has rejected the figures.
"Last night the Taliban made many attempts to enter Shutul district through the Jabal Siraj mountains, but their attempts failed, their bodies remained on the battlefield and they took only 40 bodies with them," Dashti said.
The clashes come as political efforts failed to forge an agreement between the two sides. One analyst said that such clashes will not benefit either side and there is a need to resume the negotiations between the Taliban and forces under Ahmad Massoud.
"My request is for the Taliban to show some compromise, prolong the negotiations and avoid hasty decisions on war. But this has not happened. Both sides have engaged in conflict. Why should our youth kill each other? Foreigners are no longer in the country. We should live like brothers," said Ishaq Gailani, head of the National Solidarity Movement of Afghanistan.
This comes amid negotiations between political leaders and the Taliban leadership on forming "an inclusive" government. The fighting in Panjshir intensified hours after the last US forces left Afghanistan in the early hours of August 31.