He said security forces killed six of the attackers after two of them carried out suicide attacks near the building's entrance.
"Security checkpoints around the city have collapsed in the hands of the Taliban, causing high casualties among security forces", he said.
However, another official said that "the Taliban captured several security checkpoints inside and around the city". Local residents fear the whole province may fall to the insurgents.
Afghanistan has always been torn in political, social and security turmoil, primarily due to the hostilities between government troops and the Taliban radical movement.
However, Afghanistan's intelligence agency blamed the Taliban's Haqqani Network and Pakistani group Lashkar-e-Taiba for both attacks.
Fierce fighting broke out in the pre-dawn hours of Tuesday after Taliban fighters attacked from the north and reached within three kilometers of the center of the province, according to Norulhaq Khaleqi, the spokesman for the Second Brigade of the Afghan National Army. "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.
"Government reinforcements have arrived including around 100 commando forces".
Several security forces members, including provincial deputy police chief Abdul Razaq were injured during the fighting.
"Heavy fighting continues inside the city and aircraft have just started bombarding Taliban positions", local provincial council member Jamila Amini told AFP.
Farah province, 695 km west of Kabul and bordering Iran, has been the scene of heavy clashes between Taliban and security forces over the past few months.