Taliban fighters entered the capital of northern Afghanistan’s Jawzjan province Saturday, a provincial lawmaker said, after sweeping through nine of 10 districts in the province.

The government did not deny lawmaker Mohammad Karim Jawzjani’s claim that Taliban fighters had entered Sheberghan, but said the city had not fallen. If the city falls, it will be the second provincial capital in as many days to succumb to the Taliban. Several other of the country’s 34 provincial capitals are threatened.

On Friday, the Taliban took control of the southwestern Nimroz provincial capital of Zaranj, where the government says it is still battling insurgents inside the capital.

Sheberghan is particularly strategic because it is the stronghold of US-allied Uzbek warlord Rashid Dostum, whose militias are among those resurrected to aid the Afghan national security and defence forces.

Heavy airstrikes were reported by residents of Sheberghan who also said the Taliban had freed prisoners from the city jail. They requested to remain anonymous fearing retaliation from both sides.

Taliban fighters have swept through large swathes of Afghanistan at surprising speed, initially taking districts, many in remote areas. In recent weeks they have laid siege to several provincial capitals across the country as the last US and Nato troops leave the country.

The US Central Command says the withdrawal is more than 95 per cent complete and will be finished by August 31.

The US Air Force continues to aid the Afghan air force’s bombing of Taliban targets in southern Helmand and Kandahar provinces as Afghan security forces try to prevent a Taliban takeover.

On Saturday, the US and British embassies in Kabul repeated a warning to its citizens still there to leave “immediately” as the security situation deteriorated.

On Friday, Taliban fighters assassinated Dawa Khan Menapal, the chief of the Afghan government’s press operations for local and foreign media. It came just days after a coordinated attempt was made to kill acting defence chief Bismillah Khan Mohammadi in a posh and deeply secure neighbourhood of the capital.

In a report to the UN Security Council on Friday the UN envoy for Afghanistan urged the council to demand the Taliban immediately stop attacking cities in their offensive to take more territory.

Deborah Lyons also called on the international community to urge both sides to stop fighting and negotiate to prevent a “catastrophe” in the war-torn country.

In Afghanistan’s Helmand and Kandahar provinces in the south of the country thousands of Afghans were displaced by the fighting and living in miserable conditions.

In Helmand’s provincial capital of Lashkar Gah, Afghanistan’s elite commando forces aided by regular troops were trying to dislodge the Taliban but with little success, said Nafeeza Faiez, a provincial council member. Taliban are in control of nine of the city’s 10 police districts.

Faiez said conditions for residents are desperate as they hunker down inside their homes, unable to get supplies or get to hospitals for treatment. Many of the public buildings have also been badly damaged in the fighting.

“People have no access to any service,” she said.

More than half of Afghanistan’s 421 districts and district centres are now in Taliban hands.