Taliban fighters have broken up a women’s rights march in Kabul with gunfire as bitter fighting continued in Afghanistan’s last rebel holdout and the US army’s most senior general warned that the country risked falling into wider civil war.

Camouflaged members of the Islamist militia fired shots into the air on Saturday to disperse the second protest march in as many days in the capital by Afghan women demanding equal rights from the new rulers.

“We are here to gain human rights in Afghanistan,” one protester, Maryam Naiby, told Associated Press. “I love my country.” Others in the dozen-strong march said the prophet Muhammad had given women rights, and they wanted theirs.

The Taliban have pledged to be more moderate than their previous 1996-2001 regime, which enforced a radical form of sharia law, banning women from education and employment, enforcing strict dress codes, and brutally punishing transgressors.

Officials on Saturday assured the women that their rights would be respected, but outside the the presidential palace at least a dozen special forces troops ran at the demonstrators, firing in the air and sending them fleeing.

One demonstrator said the fighters had used teargas and stun guns 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,” she said.

Farhat Popalzai, a 24-year-old student, said she was speaking for Afghan women who were too afraid to come out. “I am the voice of the women who are unable to speak,” she said. “They think this is a man’s country but it is not, it is a woman’s country too.”

The make-up of the new government remains uncertain, with any announcement pushed back until next week amid reports of heated disagreement between hardliners in the Islamist movement and those wanting to pursue a more inclusive line.

Mullah Abdul Ghani Baradar, reported by some Taliban sources to be in line to lead the new government, told Al Jazeera the new administration would include all factions of Afghans. “The government will provide security,” he said.

But Taliban fighters have painted over murals promoting healthcare and warning of the dangers of HIV, replacing them with slogans hailing victory. A Taliban spokesperson, Ahmadullah Muttaqi, said the murals were “against our values”.

North of Kabul, meanwhile, the militia’s forces pushed deep into the Panjshir valley as fierce fighting took place in the last rebel area resisting its lightning takeover of the country last month, with both sides making competing claims about their progress.

A spokesperson, Bilal Karimi, said Taliban forces now held four of Panjshir’s seven districts and were “advancing towards the centre” of the province, which held out against the Soviet Union’s occupation and also the Taliban’s first rule.

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.

In a Facebook post, Massoud insisted Panjshir “continues to stand strongly”. Praising “our honourable sisters”, he said women’s demonstrations in Kabul and the western city of Herat showed Afghans had not given up on justice and “fear no threats”.

The former vice-president Amrullah Saleh, however, warned of a “large-scale humanitarian crisis” in the province, and international observers have said the rebels’ chances of holding out against the battle-hardened Taliban army for long look slim.

But many also question the Taliban’s capacity to transform themselves from armed insurgents into the government of a country fast heading into an ovewhelming economic and humanitarian crisis.

Gen Mark Milley, chairman of the US Joint Chiefs of Staff, said he thought there was “a very good probability of broader civil war”. He said he did not know whether the movement would “be able to consolidate power and establish governance”.

Speaking to Fox News from Ramstein airbase in Germany, Milley said such a failure would “in turn lead to a reconstitution of al-Qaida, or a growth of Islamic State, or a myriad of other terrorist groups”, warning of “a resurgence of terrorism coming out of that general region within 12, 24, 36 months”.

As the international community began tentatively to engage with the new regime, the US secretary of state, Antony Blinken, was due on Monday to visit Qatar, a key player in the Afghan saga and the location of the Taliban’s political office.

Blinken will then travel to Germany to lead a 20-nation virtual ministerial meeting on Afghanistan alongside the German foreign minister, Heiko Maas. The UN secretary general, Antonio Guterres, has also convened a high-level meeting in Geneva on 13 September to focus on humanitarian assistance for the country.

Pakistan’s intelligence chief Lt Gen Faiz Hameed, who heads the powerful Inter-Services Intelligence (ISI) agency, flew into Kabul on Saturday. Washington has accused Pakistan and the ISI of backing the Taliban in the group’s two-decade fight to regain power, although Islamabad has denied the charges.

Qatar’s ambassador to Afghanistan said a technical team was able to reopen Kabul airport, which has been closed to international traffic since the end of the US-led evacuation of more than 120,000 Americans, other foreigners and Afghans deemed at risk from the Taliban.

Reuters, Associated Press and Agence France-Presse contributed to this report