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 main event of the third day of the 11th meeting of the Valdai International Discussion Club in Sochi was the closing session with President Vladimir Putin. The atmosphere was calm and open, despite the current political tensions and the Russia-West confrontation. The Russian president said that it corresponded to the spirit of the Valdai Club.