The accident on Thursday happened during testing of a liquid propellant rocket engine at a missile test site in the far northern Arkhangelsk region.
In a statement, Rosatom said the accident killed five of its staff and injured three, who suffered burns and other injuries.
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The statement came after authorities in a nearby city said the accident had caused a spike in radiation levels but the military had denied this.
Rosatom said its staff were providing engineering and technical support for the "isotope power source" of the missile engine.
The authorities have released few details of the accident at the Nyonoksa test site on the White Sea, used for testing missiles used in nuclear submarines and ships since the Soviet era.
The defence ministry initially said that six defence ministry employees and a developer were injured while two specialists died of their wounds.
The authorities in Severodvinsk, a city around 30 kilometres (19 miles) away from the test site, said on their website that automatic radiation detection sensors in the city "recorded a brief rise in radiation levels" on Thursday morning, without saying what the levels were.
The post was later taken down.
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Russian online media published unattributed video that journalists said showed a line of ambulances speeding through Moscow to take the injured to a centre that specialises in the treatment of radiation victims.
Rosatom said that the injured were being treated at a "specialised medical centre."
The Soviet Union saw the world's worst nuclear accident at Chernobyl in 1986, when the authorities sought to cover up the seriousness of the disaster.
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