The spokesman said that the police officers died during a shootout on Wednesday evening with militants at an apartment block in the town of Argun.
The spokesman said, "The police unit commander and Interior Ministry troop commander were killed in the fighting. Also two police officers, a deputy unit commander and two contract soldiers were injured."
The spokesman said the fighting had been intense and the militants set fire to the building and managed to escape in the dark, he said.
"There are indications that there are wounded among the militants," he said.
A search was launched on Thursday morning to try and trace the militants, and investigators are currently working at the scene.
Large-scale military operations are over in the North Caucasus republic, but separatists continue to carry out raids on federal troops and Kremlin-backed police and authorities. Violence often spills into neighboring Russian regions.
