Taliban fighters claim to have made gains in the Panjshir valley – one of Afghanistan’s smallest provinces and the only one not to have fallen to the Islamist militia.
Taliban spokesman Bilal Karimi said the districts of Khinj and Unabah have now fallen, giving fighters control of four of Panjshir’s seven districts.
“The Mujahideen are advancing toward the centre (of the province),” he said on Twitter.
The valley is being defended by former vice president Amrullah Saleh and Ahmad Massoud, the British-educated son of Ahmad Shah Massoud, who was killed in a suicide bombing just two days before 9/11.
Fighting in the traditionally anti-Taliban region is reported to have left hundreds dead.
Ali Nazari, a spokesperson for the National Resistance Front (NRF) fighters, told the BBC that the rebels had managed to push back the Taliban.
“There are well over a few hundred Taliban who are trapped. And they are running out of munitions and they are negotiating terms of surrender right now,” he said.
However, Taliban officials continue to claim victory.
In Kabul, two people were killed and 12 wounded after Taliban fighters fired their weapons into the air in a supposed celebration of battlefield gains.
Taliban spokesman Zabihullah Mujahid criticised the practice of firing into the air and called on the militants to stop it immediately.
The Taliban captured most of the country in a matter of days last month, following the withdrawal of US troops after 20 years of war.
Afghan women remain sceptical of the group’s promise of a more inclusive government, and more moderate rule from when they last ruled the country between 1996 and 2001.
A small number of women protested near the presidential palace in Kabul on Friday, demanding equal rights as Afghanistan’s new rulers work to form a government and seek international recognition.
Meanwhile, the economy is mired in crisis. Civil servants haven’t been paid for months, ATMs have been shut down and banks are limiting withdrawals to $200 (£144) per week, causing large crowds to form.
Aid groups have also warned of widespread hunger amid a severe drought.