Farah police spokesperson Muhibullah Muhib told Efe news that the defence and security belt of the provincial capital with the same name came under a coordinated Taliban attack from the north and northwest of the city in early hours of Friday.
The militants captured several areas on the city outskirts, he said.
The attack is a third on an Afghan provincial capital in less than a week after US special envoy Zalmay Khalilzad said that they have finalized "in principle" a peace agreement with insurgents to end the 18-year old war.
Muhib said security forces were resisting the Taliban offensive to retake the areas they captured.
"With the help of reinforcement and airstrikes, we are now pushing the militants back from the areas they penetrated in the morning," Muhib added.
The Taliban briefly took control of the Army's provincial recruitment centre before Afghan security forces retook it, Muhib said, that the militant group suffered "heavy losses" in several strikes.
"More than 50 Taliban fighters, including two commanders, were killed and several others wounded in the counter-attack," he said.
At least one policeman was also killed and several others injured in the ongoing battle, according to the spokesperson.
Interior Ministry spokesperson Nasrat Rahimi said reinforcement of special forces were sent into the city.
Rahimi said Taliban commander Noor Ahmad Chakani, the militant group's so-called deputy intelligence chief in Farah, was shot down.
Taliban spokesman, Zabihullah Mujahid claimed in a statement that their fighters launched "large-scale attacks" to capture the capital city of Farah.
Farah has been one of the most insecure provinces in western Afghanistan that borders Iran. Its capital city was attacked several times by Taliban fighters in the past two years.
Taliban militants on Saturday attacked and captured some neighbourhoods of Kudnuz city before Afghan special forces chased them away on the same day in a fighting that left 80 people dead, most of them insurgents.
A day after Kunduz, the group attacked Pul-e-Khumri, the capital city of Baghlan province but failed to enter the city after fighting the security forces on the city outskirts for several days.
( With inputs from IANS )