The gun battle followed two suicide bombings in southern Russia that have fuelled security concerns before the Games, which Islamist militants have threatened to attack.
President Vladimir Putin has staked a lot of personal and political prestige on the success of the Games, which open on Feb. 7, and has put security forces on combat alert in Sochi.
Interfax quoted sources in the security forces as saying a group of militants had been trapped in a house in the village of Karlanyurt in the Dagestan region of the North Caucasus, where insurgents are fighting to create an Islamist state.
The news agency quoted the sources as saying five officers had also been wounded in the shooting.
Dagestan's capital, Makhachkala, is about 620 km (385 miles) east of Sochi.
Russia's National Anti-terrorism Committee (NAC) declined to comment on the incident but confirmed a special operation was under way against a group of militants in Dagestan.
Mostly Muslim Dagestan is plagued by bombings and shootings that mainly target police and state officials as part of the insurgency.
At least 34 people were killed last month in the suicide bombings in the southern city of Volgograd. Putin ordered safety measures to be beefed up nationwide after the attacks.
- Unrest, Conflicts & War
- Politics & Government
- President Vladimir Putin
- Islamist militants