Interior Ministry spokesman Najib Danish said at least six security forces were killed and 12 others, including the deputy provincial police chief, were wounded in the fighting.
"If the security forces can't take control of the whole city by the end of the day, then it will be very hard to take control of the city anytime soon", he said.
Fared Bakhtawer, head of the provincial council, said several security checkpoints in the city of Farah were overrun by Taliban fighters and that an intense gun battle was ongoing.
Special police forces from Kandahar and commandos from Herat had also been deployed in Farah, Afghan officials said.
Afghan troops and police nationwide have struggled to hold back the resurgent Taliban since the withdrawal of most North Atlantic Treaty Organisation combat forces at the end of 2014.
Zabihullah Mujahid, a Taliban spokesman, claimed responsibility for the attack.
Heavy fighting has broken out in the western Afghan city of Farah after the Taliban launched a major offensive overnight to capture the provincial capital.
By midday, gunshots could be heard around Farah's central prison, intelligence department and police headquarters, only a few kilometers from the compound of the provincial governor, near the Iran-Afghanistan border.
The noise has "filled the city", said one resident who gave his name as Bilal, adding that he could see smoke rising from the direction of a building housing the NDS.
"The Afghan security forces are bringing their full capabilities, consisting of Army, Police, Commandos and Air Force, to bear on the situation", it said, adding that US forces "stand firm beside our Afghan partners and will continue to reinforce this Afghan-led offensive".
There were no detailed casualty assessments but a Resolute Support spokesman said dozens of Taliban fighters had been killed and there had also been an unspecified number of casualties on the government side. Gunfire and explosions could be heard as he spoke to an AFP reporter by telephone.
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. At least eight insurgents had been killed and three wounded, it said.
"First 1,000 Taliban insurgents attacked Farah districts on Tuesday and after the first attack over 1,000 other insurgents also joined the attack", he said.
The insurgents in a statement warned residents to remain in their homes and "stay calm".
Farah is a poppy-growing province in an isolated region of Afghanistan.
The Taliban are stepping up their spring offensive, in an apparent rejection of a peace talks overture from the government. Kunduz was subsequently retaken by the government both times.