The Taliban claim they are in complete control of the Afghan province of Panjshir, the final pocket of territory which has remained outside their rule.
There has been heavy fighting in the area, north of the capital Kabul, between the Taliban and resistance fighters.
A Taliban spokesman on Monday declared victory for the Islamist group.
But resistance fighters said they were still present in "all strategic positions" and "continue to fight".
"The Taliban haven't captured Panjshir I am rejecting Taliban claims," Ali Maisam, spokesman for the National Resistance Front of Afghanistan (NRF), told the BBC.
A tweet from the group's Twitter handle also said: "The struggle against the Taliban & their partners will continue until justice & freedom prevails."
Pictures on social media showed Taliban fighters in front of the gate of the provincial governor's compound. The BBC has not been able to independently verify them.
The Taliban took control of the rest of Afghanistan three weeks ago, taking power in Kabul on 15 August following the collapse of the Western-backed government.
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.
On Sunday, the leader of the NRF, Ahmad Massoud, said he was open to entering peace talks, as he called on the Taliban to end their offensive.
In a post on Facebook, Mr Massoud said the NRF, which includes former Afghan security force members and local militias, would be prepared to stop fighting if the Taliban ceased their attacks.
There was no response from the Taliban.
Exact death tolls are not known, but both sides have reported casualties in the fighting.
Over the weekend, 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 also died.