The Interior Ministry in the North Caucasus republic, which neighbors Chechnya, said earlier Tuesday that one gunman was killed and one arrested.
A source in the Federal Security Service (FSB) department in Ingushetia said the gunmen were notorious in the republic.
"The operation included an ambush attack ... on the gunmen who were in a car," the source said. "They were killed in the crossfire."
The Ingush Interior Ministry said gunmen in a Soviet-made silver-colored Lada car opened fire on a police vehicle at about 2:00 p.m. Moscow time (10:00 a.m. GMT) Tuesday. Police officers returned fire and managed to "neutralize" the gunmen in the ensuing skirmish.
"Sources said they were responsible for the killings of police officers in Ingushetia," the ministry said.
The FSB source said the gunmen were involved in a raid on Ingushetia in 2004 when police said 19 police precincts and prisons were attacked.
Tuesday's incident is the sixth targeting law enforcement and other officials in the republic in the week from August 23 to 29. Each time, the same silver Lada was involved, the source said.
The latest attack occurred in Nazran, Ingushetia's largest city, Monday night, when a former police chief of an anti-organized crime unit was gunned down in his car.
On August 23, a district police chief in Ingushetia, Akhmed Murzabekov, was shot three times but survived.
The attacks came against the background of a campaign in the region to give militants a chance to surrender after Russia's most wanted terrorist, Shamil Basayev, who claimed responsibility for the 2004 Beslan school massacre and other atrocities, was killed July 10.
The deadline for the voluntary surrender of militants has been extended until September 30.
Although authorities have announced that the active phase of the counterterrorism operation in neighboring Chechnya is over, violence has continued to affect the North Caucasus as a whole.
Three policemen lost their lives and two others were seriously wounded in two separate attacks in Ingushetia on Saturday, and two officers were injured in Chechnya Sunday.
