Afghan forces backed by air strikes mounted a new offensive to flush out Taliban insurgents encircling the capital of southern Uruzgan province, officials said Sunday, days after militants stormed into the city.

Taliban fighters on Thursday had attempted to overrun Tarin Kot, triggering heavy fighting around government buildings and sending panicked residents fleeing, but they were repelled hours later by Afghan forces bolstered by reinforcements.

Government troops launched a fresh offensive late Saturday to further beat them back from the outskirts of the city, which has been besieged for months.

"Dozens of Taliban fighters have been killed since military, police and special forces mounted the offensive backed by air strikes," Dost Mohammad Nayab, spokesman for Uruzgan's governor, told AFP.

He said 13 policemen were killed and 20 others wounded in recent days of fighting, which highlights the insurgent movement's aggressive push to capture big cities, from Kunduz in the north to Lashkar Gah in the south.

Boosting morale for government troops, General Abdul Raziq, the powerful police chief of Kandahar province with a fierce reputation for brutality, has been leading the operation in Uruzgan.

US warplanes also offered support, with three air strikes in the vicinity of Tarin Kot on Friday, along with Afghan air support.

But many civilians who fled the Taliban onslaught on Thursday remain fearful of returning to Tarin Kot.

"We left everything behind, including our house, farm and livestock," said Ezatullah Khpalwak who escaped to Kandahar with 25 family members when the fighting erupted.

"The government says it has driven out the Taliban from Tarin Kot, but we fear the militants will make a comeback."

In a sobering admission on Thursday, Uruzgan's police chief Wais Samim had said many of Tarin Kot's outer defences had fallen to the Taliban without a fight, suggesting internal foul play as he vowed action against any insurgent sympathisers.

The Taliban had drawn jobless Afghans from outlying districts to join them in attacking Tarin Kot, promising them free rein to loot once they were inside the city, multiple village residents told AFP.

"The Taliban announced in mosques: 'the head of the enemy will be ours, the booty will be yours'," Mohibullah, a resident of the volatile Dehrawud district, told AFP.

"That's how they attracted dozens of jobless men to fight with them."

Nayab said many homes inside Tarin Kot were looted after the Taliban raided the city on Thursday, with stolen possessions including vehicles of local residents.

The deteriorating security highlights the struggle of overstretched Afghan forces to secure remote provinces such as Uruzgan, a top poppy-growing region where Australian, Dutch and American troops fought for years.

Elsewhere in the country on Sunday, the prominent police chief of eastern Nangarhar province, an Islamic State group stronghold, was killed by a roadside bomb.

General Zorawar Zahid was leading a counter insurgency operation in the troubled Hasarak district when his vehicle hit an improvised explosive device, underlining the growing insecurity in Afghanistan. The Taliban claimed responsibility for his killing.