A clash erupted after police and the military found a group of armed men at an abandoned farm on the border between the provinces of Karachayeva-Cherkessia and Stavropol in the western part of the Caucasus, regional police spokesman Sergei Kulik said.
The suspects were behind the attack on a police car earlier this month, when three officers were killed, Kulik said.
Violence attributed to separatists seeking an Islamic state in the Caucasus is less frequent in Karachayeva-Cherkessia than in the other Caucasus provinces of Dagestan, Ingushetia and Chechnya, where police and suspected insurgents are killed almost daily.
Also Tuesday, police acting on a tip killed two suspected suicide bombers who had refused to surrender in Chechnya's capital, Grozny, said provincial police spokesman Magomed Deniyev. Explosives and detonators were found on the would-be bombers, he said.
Meanwhile, one of the 27 men wounded in Monday night's double suicide attack on a village in the eastern Caucasus province of Dagestan died in hospital, raising the death toll to three, police spokesman Vyacheslav Gasanov said Tuesday.
The attack on the village of Gubden known as a stronghold of radical Islamists killed a soldier and a police officer. It started when a female suicide bomber blew herself up as she tried to enter the Gubden police station. Several hours later, another bomber rammed his explosives-laden car near a police post.
The female bomber was identified Tuesday as Mariya Khorosheva, an ethnic Russian who had converted to Islam, Russia's top investigative agency said. She was also allegedly involved in what the authorities believe was an attempt to launch a suicide attack on Red Square on New Year's eve in late December, the agency said. Her partner, also an ethnic Russian convert to Islam, is believed to be one of the leaders of an Islamist cell in southern Russia.
The attack on Gubden was masterminded by Ibragimkhalil Daudov, an Islamist on the run whose wife killed herself in a rented Moscow apartment in late December while assembling an explosive for the thwarted New Year's eve attack, RIA Novosti news agency reported.
In recent months, Islamic militants have stepped up their attacks on military, police and civilians both in Northern Caucasus provinces and in central Russia. A 20-year-old suicide bomber from Ingushetia, another province that borders Chechnya, blew himself up at Moscow's busiest airport last month, killing 36 and wounding more than 180 people.
Human rights groups and critics of Kremlin-appointed provincial governments say that federal forces and police trigger the violence with extra-judicial killings, arrests, kidnappings and other abuses. Government critics and experts claim that young men have no other options but to join the insurgents because corrupt officials blacklist their families to extort bribes.
Czarist Russia conquered mountainous and multiethnic Northern Caucasus by the late 19th century, and many of the region's natives retained their devotion to Islam even in officially atheist Soviet times. After the 1991 Soviet collapse, the region was beset by violence, stoked by poverty, corruption, Islamist extremism and feuding criminal gangs.
Associated Press reporters David Nowak and Mansur Mirovalev contributed to this report from Moscow