The attack - the first major assault targeting a provincial capital since the Taliban announced its annual spring offensive - began when several security checkpoints were overrun after midnight, with the militants capturing one urban district and parts of another, according to provincial council member Jamila Amini.
He said security forces killed six of the attackers after two of them carried out suicide attacks near the building's entrance.
No one immediately claimed responsibility for the attack. He said fighters launched attacks form multiple directions, after which they overran several checkpoints in the city.
Local media reported that the militants take control of several government offices, including the provincial department of National Security Directorate (NDS), the country's intelligence agency.
"There is no danger of Farah city collapsing into the hands of Taliban", he added.
Scores of civilians were fleeing the city to seek safer places in the province, 695 km west of Afghan capital of Kabul, bordering Iran. The group said in April that this year's campaign, called 'Al Khandaq, ' is in response to US President Donald Trump's aggressive military strategy to force the militants into peace talks.
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Bakhtawer said casualties were high among security forces, but couldn't provide a precise number.
In the meantime, Radmanish said that "two security forces were killed in the clashes and four others were wounded", adding that "the situation would change by the afternoon and security forces have been deployed to the city".
Residents in Farah have long warned that the city was vulnerable. "An intense battle is going on in the city", he said without providing additional details. Most people are staying indoors.
Farah is a poppy-growing province in an isolated region of Afghanistan.
The Taliban have pledged to cooperate with the project.
In January, NATO's Resolute Support Mission, tasked with building up the Afghan government's security forces, assessed that almost 15 percent of the country's 407 districts - more than 20 percent of the landmass - was under insurgent control or influence, according to a watchdog report released this month.