The fighting, which punctured the patina of stability ensured by years of heavy-handed rule by the Kremlin-appointed leader, broke out hours before Russian President Vladimir Putin gave his annual state of the nation address in Moscow.
In his address, Putin said he was confident that local Chechen forces were capable of dealing with the "rebels," who he suggested were receiving support from abroad.
Security officials said militants travelling in three cars entered the republic's capital, Grozny, at 1 am local time, killing three traffic police at a checkpoint.
The agency said more gunmen were found in a nearby school and security forces were sent to "liquidate" them. No students or teachers were in the school when it was seized by the militants, RIA Novosti quoted vice principal Islam Dzhabrailov as saying.
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Russian state television showed video footage of security officers firing automatic weapons and grenade launchers at the three-story school, its windows left shattered and charred.
Chechen leader Ramzan Kadyrov, who travelled to Moscow for Putin's address, told journalists afterward that the security operation was over. "We have found the bodies of nine (militants), but they (the security officers) are continuing to search," the Interfax news agency quoted Kadyrov as saying.
In October, however, a suicide bomber blew himself up outside a concert hall in Grozny, killing five policemen and wounding 12 others as the city celebrated Kadyrov's birthday.