The Russian army says it has killed five Chechen rebels including a Turkish "mercenary" during clashes south-east of the republic's capital, Grozny.
Russian troops are frequently attacked in Chechnya
The fighting took place late on Sunday near the village of Serzhen-Yurt, army spokesman Ilya Shabalkin said.
The Turkish fighter was named as Hasan Umac and his passport was shown on Russian television.
In Grozny on Sunday rebels killed four Russian servicemen, the army said. The rebels want independence for Chechnya.
The army intercepted a radio conversation in Turkish between the rebels near Serzhen-Yurt, about 35km (22 miles) from Grozny, before ambushing them, Russian television reported.
Itar-Tass news agency said the other rebels' bodies were badly disfigured and had no documents on them, so they could not be identified.
According to Mr Shabalkin, the rebels had a map of Grozny which appeared to target a bakery.
The Russian operation followed a tip-off from a captured Algerian citizen of British origin, Kamal Rabat Burakhlya, he said.
"He told investigators where the gangs were deployed, including those that included foreign mercenaries," the spokesman was quoted as saying.
Chechen separatists have been fighting for independence from Russia for a decade.
Russian forces withdrew from Chechnya after a devastating 1994-96 war that left the North Caucasus republic crippled and de facto independent. But the army stormed back into Chechnya in September 1999, following a rebel incursion into neighbouring Dagestan.