The spokesman said one officer was injured on Tuesday when unknown assailants armed with automatic weapons opened fire on police in southeast Chechnya's Vedeno District.
The second incident occurred a few hours later in the Achkhoi-Martan District in the southwest of the republic when two officers were injured in shootout with militants near the village of Bamut.
One militant was killed during the exchange of fire.
Russia's North Caucasus republics have seen a rise in violence of late. Attacks on federal forces and police are an almost daily occurrence. Monday saw the worst attack in the region for years when a suicide bomber rammed an explosives-laden minivan into the gates of a police station, killing over 20 officers.
The Kremlin officially ended its anti-terrorism operation in Chechnya in April. The republic saw two brutal separatist wars in the 1990s and early 2000s.
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