Russian media say police have shot dead an insurgent in a brief gunbattle in the southern town of Nalchik.
The man was reportedly killed when he and three others fired on a police patrol that stopped them to check their documents.
Security forces have been combing Nalchik, capital of the Kabardino-Balkaria republic, for the remnants of a force that raided the town last Thursday.
Chechen warlord Shamil Basayev used a rebel website to claim responsibilityfor the attack that killed dozens of police and civilians.
He said it was carried out by fighters under the so-called Caucasus Front of Chechen rebels, adding that 14 rebel fighters were killed. Police said 90 militants, 35 police officers and nine civilians died.
Basayev previously claimed responsibility for the Beslan school siege that resulted in the death of 330 people in North Ossetia last September.