After more than five hours of battle on Thursday, Russian officials proclaimed victory and said that all seven, including their leader, had been killed in the assault.
Two members of the elite SOBR unit were wounded.
"Today we carried out a successful operation against (the armed group) Yarmuk and its leader Muslim Atayev," Russian Deputy Interior Minister Arkady Yedelev said in front of the smouldering building.
He added that two women were among the dead, who were "active members of the group and were also armed". A local interior ministry official earlier had said that four of the seven fighters killed were women.
Ready to die
After negotiations failed to secure the surrender of the fighters, who had been surrounded since late Tuesday in the building on the outskirts of Kabardino-Balkaria's regional capital Nalchik, elite troops started an assault about 8.30am (0530 GMT).
"Inshallah (God Willing!) we will triumph in any case: either we will repulse the enemy or
go to heaven"
Message on kavkazcenter.com
Police suspect the fighters belonged to the Muslim group known as Yarmuk. Atayev was killed along with his wife, ITAR-Tass reported.
In an e-mail posted on the Chechen separatist website, kavkazcenter.com, Yarmuk said it was resisting the Russian assault on its hideout but said all its members were ready to die.
"Inshallah (God Willing!) we will triumph in any case: either we will repulse the enemy or go to heaven," the text said.
The website said that after four hours of fighting, five Russian special forces troops had been killed and another 10 wounded. It made no mention of the fighters killed.
Separately, four Russian soldiers were killed in the past 24 hours in two incidents in Chechnya, an official in the pro-Moscow Chechen administration told AFP on Thursday.
The North Caucuses continue to
be a plagued by separatist wars
Two soldiers died in an explosion of a landmine they were trying to defuse near Nozhai-Yurt in east of Chechnya on Wednesday, the official said.
Two others were killed and two more were wounded on Wednesday in an ambush of their military convoy near Dyshny-Vedeno in the southeast, the official added.
About 80,000 Russian troops are based in and around Chechnya, where a separatist war continues to rage more than five years since the latest conflict in the breakaway republic began.