Heavy gunfire in the village of Ordzhonikidzevskaya - just over the border from Chechnya in the region of Ingushetia – lasted for over forty hours, ending on Sunday.
Ilya Shabalkin, spokesman for the Russian military in the Caucasus, said: "These people, acting on Basayev's orders ... were involved in recruiting and training young women from various regions in the North Caucasus."
In a statement to the Itar-Tass news agency, Shabalkin also claimed the separatists were trying to recruit "suicide bombers".
Among those killed was 27-year-old Muhammad Khazhiyev, a religious leader of an Islamist community in Ingushetia's Sunzhensky region.
Increased military presence
In the last few weeks Moscow has also intensified a hunt for separatists, especially Basayev - Russia's most wanted man security services say is organising resistance.
Shabalkin denied earlier reports the separatists had killed a number of hostages they held in the house during the shootout.
Russian soldiers also suffer
casualties on almost daily basis
There was no official word on casualties on the Russian side.
However kavkazcenter.com website said at least two Russian soldiers were killed and six seriously injured.
In a separate operation early on Sunday, Russian troops killed a separatist in the Chechen capital Grozny who Russian security services said could be linked to a bomb attack on Ingush President Murat Zyazikov on 6 April.
Zyazikov was not killed in the attack.
Russia has been fighting separatists in the southern region of Chechnya for a decade and, although it says it is restoring control, loses policemen and soldiers daily.
In recent months, fighting has spilled over into Ingushetia, inhabited by a people closed related to Chechens.