0803 GMT January 19, 2019
The US carried out more drone strikes overnight and the Afghan Army is still clearing the city, Afghan and NATO officials said, AFP reported.
Shops, offices and schools remain closed, with residents frightened to leave home after hours of heavy fighting.
"The Taliban have retreated from the city and positioned their forces in the outskirts," provincial council member Dadullah Qani said from Farah.
Fighting continued late into the night, he said. "The city is still closed as people are in fear."
With Internet and mobile networks patchy, casualty figures were difficult to verify.
Defense Ministry spokesman Mohammad Radmanish said 11 soldiers have been killed. Previously he and NATO had said "dozens" of Taliban were killed in the fighting.
Farah 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.
Reinforcements including special forces were rushed in from Herat and Kandahar as the fighting began late Monday.
Aref Rezaee, a spokesman for the 207th Corps, said that with their help the Taliban were forced from the city at around midnight, some 24 hours after residents said the initial assault began.
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.
The assault is the latest in a series of attempts by the Taliban to capture urban centers. Kunduz, Afghanistan's fifth largest city, fell briefly to the Taliban in 2015.
The Taliban, along with Daesh, have also stepped up their attacks in the capital Kabul, which the UN says has in recent years become one of the country's deadliest places for civilians.