Kabul, Afghanistan - Reports of fighting emerged on Tuesday from the one part of Afghanistan not under Taliban control, even as the fundamentalist group asserted its control in Kabul, hours after the final US troops ended the country's 20-year presence there.

Resistance fighters in Panjir have reported a new offensive by Taliban forces.

About seven or eight Taliban fighters died in the Monday clash, according Fahim Dashti, a spokesperson for the forces in Panjir. He also noted that many people had been wounded on his side.

Panjir is the only district that was not taken in the Taliban's offensive this month. Nor was it taken from 1996 to 2001, partially because the region is only accessible through a valley that is relatively easy to defend.

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The Taliban made no comment. It has made relatively few assaults on Panjir, even as it took over the rest of the country.

A high-level meeting of the Islamist group's leadership council had taken place over the weekend, according to a Taliban spokesman.

Important consultations on the formation of a new Islamic government and cabinet were part of the discussions, he added, spurring speculation that the country's new leadership will be unveiled soon.

Meanwhile, Kabul residents reported calm in the Afghan capital on Tuesday, in the wake of the US departure.

"The city is quiet," said Lotfullah, who lives in central Kabul. Most shops in the Shahr-e Nau district were open, but only have a few customers, he said.

A few banks reopened their largest branches on Tuesday, just more than two weeks after the Taliban reconquered the country, and hundreds of people stood in line to withdraw money.

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In the streets, few members of the Taliban were in evidence. Most were guarding buildings, mainly government offices.

One resident of the Dasht-e Barchi district in western Kabul said private and public schools had reopened for the first time since the Taliban took power in mid-August.

All pupils up to the sixth grade have returned to school, he said.

A day earlier, the final US troops left Kabul, bringing to an end a tense evacuation mission and a 20-year war in Afghanistan.

Although the US had begun planning its departure in 2020, after a deal between the Trump Administration and the Taliban, when President Joe Biden carried on with the plan, he had expected to hand control to a Western-backed government, not the people the US had been fighting for two decades.

Taliban members are jubilant. Its forces have occupied the city's airport, which had been the last haven of US control as Washington and its allies executed a desperate airlift operation for the last two weeks to get Westerners and their allies out of the country.

Taliban members guarding the airport now are virtually indistinguishable from the US troops who had guarded it up until Monday, having raided abandoned supplies and making use of uniforms and equipment left behind.

"We're writing history again. The 20-year occupation of Afghanistan by the US and NATO ended this evening. God is great," was one cry.

But the Pentagon was nonplussed about the abandoned weapons and munitions.

"We made sure to demilitarize, to make unusable, all the gear that is at the airport - all the aircraft, all the ground vehicles," said spokesperson John Kirby. "The only thing that we left operable are a couple of fire trucks and some forklifts, so that the airport itself can remain more operational going forward."

"So I think we're not overly concerned about these images of them walking around," he said, referring to images circulating since the US departure of Taliban forces exploring the airport.