"The Taliban are moving very fast, if the government does not take serious and speedy action, the province is going to collapse to Taliban", said Hamidullah, a resident of the city reached by telephone.
Located along one of the country's most lucrative drug routes, between Helmand province in the south and Iran to the west, the province has been embattled for months. In 2017 insurgents tried three times to overrun the capital, according to the Afghanistan Analysts Network.
A resurgent Taliban, largely dependent on narcotics revenues, has expanded its territorial control over parts of Afghanistan since the withdrawal of most worldwide combat forces at the end of 2014.
He said the attack happened late Monday night in Puli Alim the capital of the province.
The attack on Farah is the first siege of a provincial capital this year.
The Afghan Defense Ministry said in a statement Tuesday that Afghan security forces were able to repel their attacks.
A local administrator said the attack by Taliban insurgents was an example of intelligence failure.
The U.S. -led military coalition in Afghanistan said in a tweet that it was providing air support to Afghan forces around Farah.
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But inside the city residents reported clashes were continuing.
There were no immediate casualty assessments but residents said there were wounded and dead on both sides as well as among the civilian population.
The United States' renewed campaign against the Taliban has so far failed to curb the group's advance, which has occurred largely in rural areas, and the militants maintain strongholds throughout the south.
The assault comes as the Taliban are stepping up their spring offensive, in an apparent rejection of a peace talks overture by the Afghan government.
Mohammad Radmanish, a spokesman for the defence ministry in Kabul said they have ordered security forces from neighbouring provinces to travel to Farah to protect civilians and government buildings.
Mujahid said Taliban fighters launched a multipronged attack and overran a large number of checkpoints belonging to Afghan security forces in the city.
Farah, Ghor, Baghlan, Nangarhar and Zabul are among 10 provinces that have witnessed ongoing heavy clashes between security forces and Taliban in recent days and the continuation of the clashes have raised concerns among the people, MPs and politicians.