A heavy firefight broke out early on Sunday morning, said an officer in the Interior Ministry department in Nalchik, the capital of Kabardino-Balkariya, where the day-old stand-off came to an end.
Security forces used grenade launchers to lob canisters of tear gas into the building before entering, he said.
The forces broke down the metal door to the second-floor apartment, but retreated due to a high concentration of gas as well as smoke from a fire that had broken out.
Officers finally entered the apartment after the blaze was extinguished, finding three bodies. No information was immediately released as to the identities or nationalities of the three.
The incident is the latest in a series of confrontations between law-enforcement authorities and alleged extremists in the volatile North Caucasus region, which includes Chechnya.
Last month, security forces killed seven alleged Islamic fighters in the same city in a two-day battle with members of the so-called Yarmuk group.
Ammunition and literature
Meanwhile in a separate operation in Nalchik, 1400km (870 miles) south of Moscow, three people were detained on Saturday in a private house and police confiscated one gun, four grenades and Islamic literature produced by the conservative Wahhabi sect, according to a duty officer for the southern district office of the federal Interior Ministry.
The detainees, who included two women, were seized without any violence, the officer said. One of the women was a Chechen, while the other two detainees were from Karachayevo-Cherkessiya, another troubled region in southern Russia.
Yarmuk is an Islamic group affiliated with rebel Chechen leader Shamil Basayev. It was blamed in a December 2004 attack on an office belonging to the Federal Drug Control in Nalchik, when raiders killed four of the agency's employees, looted its arsenal and set the office ablaze.
Russia's southern provinces have been plagued by a spillover of violence from Chechnya, including the September school hostage-taking in the city of Beslan in which 330 people were killed.