The group say the Taliban targeted them with tear gas and pepper spray as they tried to walk from a bridge to the presidential palace.
But the Taliban maintain the protest got out of control, according Afghan media outlet Tolo news.
It’s the latest of several protests by women in Kabul and Herat.
The women were calling for the right to work and to be included in the government. The Taliban say they will announce the make-up of their administration in the coming days.
The Taliban have said women can be involved in government, but not hold ministerial positions.
“Twenty-five years ago, when the Taliban came, they prevented me from going to school,” journalist Azita Nazimi told Tolo.
Another demonstrator, Soraya, told Reuters: “They also hit women on the head with a gun magazine, and the women became bloody.”
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Clashes have meanwhile continued in the Panjshir Valley, north of Kabul, where resistance fighters have been thwarting efforts by the Taliban to exert control.
But there’s been claim and counter-claim. The Taliban maintain they’ve taken control of two more districts and are heading for the centre of the province.
The Panjshir Valley, home to between 150,000 and 200,000 people, was a centre of resistance when Afghanistan was under Soviet occupation in the 1980s and during the Taliban’s previous period of rule.
The NRF’s leader, Ahmad Massoud, praised protests by women in Herat, and said Panjshir continued to resist.
None of the claims by the NRF or the Taliban could be independently verified.
In a further sign of Kabul’s airport resuming activity following the US withdrawal last week, Afghan airline Ariana announced the resumption of internal flights to three cities: Herat, Mazar-i-Sharif and Kandahar.
Al-Jazeera TV quoted Qatar’s ambassador as saying a technical team from Qatar had succeeded in reopening the airport to receive aid flights.
The head of Pakistan’s spy agency, the ISI, General Faiz Hameed has arrived in Kabul, but gave nothing away when questioned by reporters.
An official told Reuters earlier this week he could help the Taliban reorganise the Afghan military.
The ISI has been accused by Western powers of backing the Taliban, something denied by Pakistan.