"NDS forces in their headquarters are engaged in heavy clashes with the Taliban".
He said more than 10 militants have been killed, and five security forces wounded.
However, Afghanistan's intelligence agency blamed the Taliban's Haqqani Network and Pakistani group Lashkar-e-Taiba for both attacks.
"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.
Afghan security forces have struggled to hold back the resurgent Taliban since the withdrawal of North Atlantic Treaty Organisation combat forces at the end of 2014. "The city is closed, people are panicked and in a state of fear".
Defense ministry officials sought to quell panic as local media reported some residents were fleeing the city. "There is no extra force to help us and the situation is getting worse", Mr. Bakhtawar said.More news: Severe thunderstorms possible today for Greater Williamsburg
Local reporters said the city was empty and shops, schools and government offices are closed as people hid inside their houses.
"Fresh commando forces are now deployed to Police HQ, NDS and Prison in #Farah".
A counter offensive operation was in progress as security forces try to bring the situation under control.
One Taliban militant has been killed and two others wounded during a separate clash erupted in Suzma Qala district of northern Sar Pul province.
The insurgents have tried several times to take provincial capitals in recent years, including in Kunduz and Lashkar Gah. "But I know the police chief might be in the front line fighting off the Taliban".
Taliban launched their spring offensive, called al-Khandaq, last month.