Resistance forces holed up in the Panjshir Valley against the Taliban have called for a ceasefire. There are reports that Resistance forces leaders have suffered heavy losses at the weekend.
The National Resistance Front said that it has proposed the Taliban stop its military operations in Panjshir and withdraw its forces. "In return, we will direct our forces to refrain from military action," it said.
The resistance group's statement said that its leaders are ready to enter peace talks.
Ahmad Massoud said he supported a plan, put forward by religious clerics, for a negotiated settlement, and called on the Taliban to end their offensive.
Earlier, reports suggested the Taliban had rapidly gained ground in Panjshir. The province, north of the capital Kabul, is the most prominent example of resistance to Taliban rule.
In a post on Facebook, Massoud said the National Resistance Front of Afghanistan (NRF), which includes former Afghan security force members and local militias, would be prepared to stop fighting if the Taliban ceased their attacks.
Panjshir, a rugged mountain valley, is home to between 150,000 and 200,000 people. It was a centre of resistance when Afghanistan was under Soviet occupation in the 1980s and during the Taliban's previous period of rule, between 1996 and 2001.
The NRF said its spokesman Fahim Dashti and a commander, Gen Abdul Wudod Zara, had been killed in the conflict, while a prominent Taliban general and 13 bodyguards had also died.
The Taliban took control of the rest of Afghanistan three weeks ago, taking power in Kabul on August 15 following the collapse of the Western-backed government.
Earlier, the Taliban said their forces were now in the provincial capital, Bazarak, where they inflicted "numerous casualties", though this was disputed by the NRF.