The deaths were not linked to the mass street protests against government waste and corruption currently sweeping the country, but will add to concerns about security in Brazil in the run up to next year's World Cup.
"Five suspects, three residents and one elite policeman died in total," a military police spokeswoman told AFP.
At least nine people were injured and nine others detained Tuesday, including the main suspect in the killing of the police officer, he added.
An officer of the military police's special operations squad BOPE and a resident were fatally shot late Monday as the police unit targeted criminals shaking down motorists caught in a demonstration, officials said.
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Police said five suspects were killed early Tuesday when BOPE moved to arrest those believed to have been involved in the attacks on motorists. Two residents who had been rushed to hospital with injuries subsequently died.
Several people were detained Monday and Tuesday.
Authorities have deployed some 1,000 security personnel to the area, backed by an armored vehicle.
Rio is one of the host cities of the World Cup, and Brazil is under pressure to improve security for the tens of thousands of tourists the tournament is expected to attract.