A truck with National Resistance Front markings is seen on a mountain top near Panjshir Valley, Afghanistan. Reuters

Taliban fighters have advanced deep into Afghanistan's holdout Panjshir Valley north of Kabul, as the top US general warned of a "civil war" if they failed to consolidate power.

Italian aid agency Emergency, which runs a hospital in Panjshir, said Taliban forces had reached the village of Anabah, where they run a surgical centre.

"Many people have fled from local villages in recent days," Emergency said in a statement on Saturday, adding it was continuing to provide medical services.

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"There has so far been no interference with Emergency's activities," it said.

"We have received a small number of wounded people at the Anabah Surgical Centre."

Members of National Resistance Front observe from a house near Panjshir Valley, Afghanistan. Reuters

Anabah lies some 25 kilometres (15 miles) north inside the 115-km-long valley, but unconfirmed reports suggested the Taliban had seized other areas too.

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.

Taliban forces control four of the province's seven districts.

The top US general told US media on Saturday “Afghanistan will ‘likely’ erupt in civil war, warning that those conditions could see a resurgence of terrorist groups in the country.

As American forces began their withdrawal, the Taliban took over Afghanistan in a lightning campaign, with only the northern province Panjshir holding out against them.

"My military estimate... is that the conditions are likely to develop of a civil war," General Mark Milley, chairman of the Joint Chiefs of Staff, told Fox News.