Saturday's stand-off in Nalchik, the capital of the Kabardino-Balkariya region, was the latest in a series of confrontations between law-enforcement authorities and alleged fighters in the volatile North Caucasus region, which includes Chechnya.
Last month, security forces killed seven alleged fighters in the same city in a two-day battle with members of the so-called Yarmuk group.
A duty officer at the southern district office of the Interior Ministry said the fighters, thought to be in the house on Saturday, were also members of the Yarmuk group.
An armoured personnel carrier and riot police were at the scene, and security forces evacuated residents of surrounding buildings and cut off natural gas flows in the neighbourhood.
A spokesman for the Nalchik police department, who did not give his name, told Ekho Moskvy radio that 20 fighters were thought to be in the apartment.
Sergei Polyansky, spokesman for the southern district office, said operations were also under way in several other districts of Nalchik to seal off other residential buildings.