Taliban and opposition forces battled to control the Panjshir Valley north of Kabul, the last Afghan province holding out against the regime, as the top US general warned of a "civil war" if the Taliban failed to consolidate power.
Both sides claimed to have the upper hand in Panjshir but neither could produce conclusive evidence to prove it.
The Taliban, which swept through the country ahead of the final withdrawal of US-led forces this week, were unable to control the valley when they ruled Afghanistan from 1996 to 2001.
Taliban spokesman Bilal Karimi said the districts of Khinj and Unabah had been taken, giving Taliban forces control of four of the province's seven districts.
But the National Resistance Front of Afghanistan, grouping forces loyal to local leader Ahmad Massoud, said it surrounded "thousands of terrorists" in Khawak pass and the Taliban had abandoned vehicles and equipment in the Dashte Rewak area.
Front spokesman Fahim Dashti added "heavy clashes" were going on.
In a Facebook post, Massoud insisted Panjshir "continues to stand strongly".
Praising "our honourable sisters", he said demonstrations by women in the western city of Herat calling for their rights showed Afghans had not given up demands for justice and "they fear no threats".
US General Mark Milley, chairman of the Joint Chiefs of Staff, underscored the tenuous situation.
"My military estimate is, is that the conditions are likely to develop of a civil war. I don't know if the Taliban is going to be able to consolidate power and establish governance," Milley said.
Speaking to Fox News from Ramstein Air Base in Germany, Milley said if they cannot that will "in turn lead to a reconstitution of Al Qaeda or a growth of ISIS or other myriad of terrorist groups" over the next three years.
Emergency, an Italian medical aid organisation, said Taliban forces had pushed further into the Panjshir Valley on Friday night, reaching the village of Anabah where the group has medical facilities.
"We have received a small number of wounded people at the Anabah Surgical Centre," Emergency said in a statement, adding that many people fled in recent days.
It was not immediately possible to get further independent confirmation of events in Panjshir, which is walled off by mountains except for a narrow entrance.
Celebratory gunfire resounded in Kabul on Friday as reports spread of the Taliban's takeover of Panjshir. News agencies said at least 17 people were killed and 41 hurt.
Pakistan's spy chief Lieutenant General Faiz Hameed flew into Kabul on Saturday. It was not clear what his agenda was, but a senior official in Pakistan said earlier in the week that Hameed, who heads the powerful Inter-Services Intelligence (ISI) agency, could help the Taliban reorganise the Afghan military.
Washington has accused Pakistan and the ISI of backing the Taliban in the group's two-decade fight against the US-backed government in Kabul, although Islamabad has denied the charges.
In Kabul, Taliban fighters broke up a demonstration by about a dozen women urging the group to respect women's rights to education and jobs, according to private broadcaster Tolo news.
Footage showed women confronted by armed militants covering their mouths and coughing, and one demonstrator said the fighters had used tear gas and tasers against the participants, who had been carrying banners and a bouquet of flowers.
"They also hit women on the head with a gun magazine, and the women became bloody," said a demonstrator who gave her name as Soraya.
The Taliban imposed violent punishments and barred women and older girls from school and work when previously in power, but have sought to present a more moderate face this time.
GOVERNMENT NEXT WEEK
A Taliban source said the announcement of a new government would be pushed back to next week.
Taliban co-founder Mullah Abdul Ghani Baradar, reported by some Taliban sources to be in line to lead the new government, said in remarks on Qatar's Al Jazeera channel that the new administration will include all factions of Afghans.
"We are doing our utmost efforts to improve their living conditions. The government will provide security, because it is necessary for economic development," he said.