The gunmen opened fire from two Russian-made Zhiguli cars at police officers, who were conducting a sweep of an area where a suspected militants' hideout had been earlier located.
"All suspected militants have been eliminated in the exchange of fire," the source said.
The bodies are now being identified. A vehicle search revealed a large number of weapons, ammunition and explosives.
The source did not confirm or deny earlier reports that two police officers were wounded in the skirmish.
Ingushetia neighbors troubled Chechnya and during the first eight months of 2008 saw a sharp increase in assaults on law enforcement and military personnel.
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The clash of Russian and Western interests has given rise to a geopolitical battle. German politicians are trying to leave all doors and windows open for dialogue with Russia. Moscow does acknowledge this, and Germany is probably the only country with which it is ready to discuss European security.