Revealing the incident on Tuesday, Russia's defence ministry said the men died from smoke inhalation.
Authorities refused to say whether the vessel was nuclear powered, raising concerns over possible radiation leaks.
Dmitry Peskov, President Vladimir Putin's spokesman, said details about the vessel were "totally classified".
"There is nothing illegal about this. It fully corresponds to the Russian law on state secrets," he said.
Defence authorities said the vessel was a navy research submersible that was taking measurements in Russian waters.
But Russian independent media outlets reported that it was a small nuclear-powered submarine, naming it as the AS-12 Losharik. US officials said the vessel was designed to cut undersea cables.
The craft is now at Severomorsk, the main base of Russia's Northern Fleet on the Barents Sea, The port was also home to the Russian Kursk nuclear submarine, which sank in 2000 killing 118 sailors.
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