He said 10 Taliban militants were killed.
Afghan special operations forces, army and police, supported by US airpower, had started clearance operations on the city's outskirts, USA and Afghan officials said.
The Taliban has launched a major offensive to capture a city in western Afghanistan, with heavy fighting breaking out in the area, officials say.
Fared Bakhtawer, head of the Farah provincial council, said the insurgents overran several security checkpoints in the provincial capital of the same name and that heavy fighting was underway. He said casualties were high but couldn't provide a precise number.
It was the first Taliban assault on a provincial capital this year after it announced the start of its annual spring offensive last month and formally rejected Afghan government peace initiatives.
Taliban also claimed capturing many areas of Farah including the third police district and the NDS headquarter.
Farah borders Helmand province where the Taliban control multiple districts. "Gun battles, air strikes and explosions are taking place around the city", he told Xinhua earlier by phone.
There was no immediate confirmation from NATO's mission in Kabul.
"Six security forces members were martyred in Farah city, " Interior Ministry spokesman Najib Danish told local media Tolo News TV.More news: Google Accused of Harvesting Data from Millions of Australian Android Users
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Radmanish said: 'The situation is under control and will change by the end of the day'.
Inside the city residents reported clashes were continuing.
At least some militants have been hiding in private houses, making it hard for Afghan forces to use heavy weapons, Farah governor Abdul Basir Salangi told Ariana News, adding: "But still we are taking back positions one by one".
Farah province has seen heavy fighting in recent months, with local officials and tribal elders requesting addition forces from the already overstretched army and police.
"Taliban has entered our city with a full might. they are equipped with heavy arms and night vision", said Dadullah Qane, a provincial council member of Farah.
The insurgents in a statement warned residents to remain in their homes and "stay calm".
Many radio and television channels in the province have stopped broadcasting, fearing for their employees' lives, according to media watchdog Nai.
Despite security concerns, the Taliban have pledged to cooperate with the gas project.
But it has been the scene of intense fighting in recent years.