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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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.