But the defence ministry said the army had repulsed the attack and that "security forces are now chasing the enemy".
An unnamed local government official and several residents said fighting between security forces and militants was under way around 4 kilometers from the city center.
The attack, which comes as the Taliban step up their annual spring offensive, began around midnight, with the insurgents capturing one district and parts of another, local provincial council member Jamila Amini told AFP Tuesday from inside the city.
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"There is no fear of losing Farah city to the militants", he said, adding that Special Operations Forces and army commandos together with army reinforcement have arrived in Farah city.
Attaullah Khogyani, the governor's spokesman, told Pajhwok Afghan News the assault ended with the killing of eight armed attackers at 6: 40am.
"The sounds of explosions and gunfire have filled the city", one resident who gave his name as Bilal said, adding that he could see smoke rising from the direction of a building housing the NDS.
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Mohammad Sarwar Osmani, a lawmaker form Farah province, also confirmed the Taliban attacks. "We assure the people of Farah that all necessary operations have been implemented and Afghan air force, commando force, and contingents of Corp in western Afghanistan are in action against security threats", defense ministry officials said in a statement.
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.
Several security forces members, including provincial deputy police chief Abdul Razaq were injured during the fighting.
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Since then, Afghan security forces have suffered heavy casualties at the hands of the insurgents but claim they have inflicted heavy damage on the Taliban in return.