"Subdued" fighting was continuing outside the city and Afghan troops were being supported by US airpower and advisers, a NATO spokesman said, while the Afghan army was conducting a clearing operation inside.

Some residents were starting to emerge from their homes, though many remained indoors, frightened by the hours of gunfights, airstrikes, and explosions that began overnight Monday to Tuesday.

"People are scared but happy there is no more fighting in the city," Bilal, an NGO worker, told AFP. "I can see the people have started going about their business in the city, but government offices are closed."

With internet and mobile networks patchy, casualty figures were difficult to verify.

Defence ministry spokesman Mohammad Radmanish said 11 soldiers had been killed. Previously he and NATO had said "dozens" of Taliban died in the fighting.

Farah provincial governor Abdul Basir Salangi and interior ministry spokesman Najib Danish gave far higher tolls. Danish said 300 Taliban had been killed, though Salangi said the 300 figure also included the wounded.

Salangi's spokesman, Nasir Mehri, said at least five civilians had been killed, and gave a higher death toll for the security forces of 25.

The attack was the latest in a series of attempts by the Taliban to storm urban centres.

Farah province, a remote poppy-growing region that borders Iran, has been the scene of intense fighting in recent years, and there have long been fears that its capital is vulnerable.

- Troops rushed in -

Reinforcements including Afghan special forces were rushed in from Herat and Kandahar as the fighting began late Monday.

A spokesman for NATO's Resolute Support mission in Afghanistan, Lt Col Martin O'Donnell, said the US had carried out drone strikes and had A-10 Thunderbolts in the air over the city as a show of force supporting the Afghan army during the fighting.

Aref Rezaee, a spokesman for the 207th Corps, said the Taliban were forced from the city at around midnight, some 24 hours after residents told AFP the initial assault began.

But some insurgents are believed to be hiding inside residents' homes, spurring speculation the clearance operation could take some time.

"There is fear that once the reinforcements are gone they will come out and launch an attack again," Jamila Amini, a provincial council member, told AFP from inside the city.

Many remained apprehensive. "I want to open my shop today but they have planted land mines in some parts of the city," said resident Abdul Samad.

Afghan forces, their numbers sapped by killings and desertions, have been struggling nationwide to hold back the resurgent militant group since the withdrawal of NATO combat forces at the end of 2014.

The assault is the latest in a series of attempts by the Taliban to capture provincial capitals. Kunduz, Afghanistan's fifth largest city, fell briefly to the Taliban in 2015.

The insurgents, along with the Islamic State group, have also stepped up their attacks in the capital Kabul.