Fresh fighting has been reported in Afghanistan's Panjshir Valley, the final pocket of territory which remains out of the hands of the Taliban.
One of the resistance leaders in the valley, Amrullah Saleh, dismissed reports that the Taliban had captured it as "baseless".
But he admitted conditions are difficult, with the Taliban closing phone, internet and electricity lines.
The fighting comes with the Taliban set to finalise a government, reports BBC.
Panjshir Valley, north of the capital Kabul, is one of Afghanistan's smallest provinces and the only one not to have fallen to the Taliban.
The traditional anti-Taliban stronghold is home to somewhere between 150,000 and 200,000 people, and is hidden behind mountain peaks.
The resistance - which includes former Afghan security force members and local militias - is led by local tribal leader Ahmad Massoud. His father successfully fought the Soviets who invaded in the 1980s, and the Taliban in the 1990s.
In a video message sent to the BBC, Mr Saleh, a former vice-president of Afghanistan, said there had been casualties on both sides.
"There is no doubt we are in a difficult situation. We are under invasion by the Taliban," he said, adding that his forces would not surrender.
But resistance leaders concede that some districts have fallen to the Taliban, while pro-Taliban social media showed clips seeming to show their fighters with captured tanks and other military gear.
Rumours that the Taliban had captured Panjshir prompted celebratory gunfire to ring out in Kabul and other cities, reportedly killing a number of people.
A Taliban spokesman said fighters should "avoid firing in the air and thank God instead".