In the latest violence, Russian news agencies reported on Thursday that two senior police officers were killed during a search for “bandits” in a house in the Ingush town of Malgobek.
Three armed men were also killed and several were detained.
Police have been hunting insurgents who last week seized control of large parts of Ingushetia, killing nearly 100 people.
Many of those who led last week’s raids were Ingushetians allegedly allied to Chechen separatists whom Moscow has been battling for a decade.
Those raids dealt another blow to the Kremlin which is struggling to crush the Chechen movement and stop it from spreading.
Many in the region blame the hard line policies of Russian President Vladimir Putin for the spread of the war beyond Chechnya’s borders.
He repeatedly said he ‘will not negotiate’ with separatists
In Chechnya itself, two policemen died when their car drove near a landmine in the local capital Grozny.
Earlier, a separate explosion near a factory in the city killed two people.
Russia has been trying to subdue the Chechens for a decade, dispatching large contingents of troops to the mountainous region twice since the collapse of Soviet rule.
Moscow keeps about 70,000 troops in Chechnya.
Putin has repeatedly said he ‘will not negotiate’ with separatists.
But his plans to resolve the conflict by offering the province broad autonomy was badly dented by the assassination in May of Chechnya’s Kremlin-backed president.