An explosion during the operation injured two special police officers, while a third suspect was detained alive, reports said.
"Law enforcement officers stopped a car, two suspects resisted arrest and were liquidated on the spot. Explosives were found in the car," TASS state news agency quoted a source as saying.
The special operation is reportedly taking place in a residential area of Nizhny Novgorod, an industrial city of more than 1 million on the banks of the Volga River, around 400 kilometres (250 miles) east of Moscow.
Russia says 'concerned' at fighters' refusal to leave Aleppo
A law enforcement source told RIA Novosti: "They have shot dead two (people) suspected of terrorism. They were driving in a Daewoo Nexia car. Now FSB (security force) officers are working at the scene."
There was no immediate official confirmation of the reports. Such special operations are frequent in Russia's volatile North Caucasus but are rare in the central region where most Russians live.
A law enforcement source quoted by TASS named those killed as "members of illegal armed groups," a term also used by officials to describe insurgents in the North Caucasus.
Two special police officers were wounded in an explosion during the operation, TASS reported, citing a local police source.
"The officers suffered blast injuries as the result of an explosion. They have been taken to hospital, the source said.
A third suspect was detained alive, Interfax news agency said, quoting a regional law enforcement official.
A Rossiya 24 state television correspondent reported that details of the incident would only be released on Monday.
The regional branch of the FSB security service told Interfax news agency that "until urgent investigative steps are finished, we will not comment. Later we plan an official press release."
Local media posted photographs from social networking sites apparently showing two bodies lying on the ground close to a car with doors open, as vehicles and security officers block the nearby road in a suburb called Tsvety.
A robotic device can also be seen in the photograph. TASS reported that the anti-mine robot was used to neutralise an explosive device in the car.
A local resident told Interfax that he heard shots in the morning between 8 and 9 am and security forces told people living in the residential area not to leave their homes.
In August Russian special forces raided an apartment building in the second largest city of Saint Petersburg in an operation targeting North Caucasus militants, killing four suspects.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ