The MIR radio station said the hacking, which it called "an absolute fake and a provocation," had lasted around 40 minutes.
The fake message, still circulating on social media, said that "Ukrainian troops armed to the teeth by NATO and with Washington's consent and support have invaded the Kursk, Belgorod and Bryansk" territories.
The voice, very similar to Putin's, also announced martial law, general mobilization and the evacuation of civilians in those three regions.
"This was indeed a hack," Kremlin spokesman Dmitry Peskov was cited as saying by state-run agency RIA Novosti.
"Control has already been restored."
The Belgorod region administrative center said the message was a "deep fake" aiming to "sow panic among peaceful Belgorod residents."
The Voronezh region neighboring Belgorod also warned its residents of a "hacking of radio broadcasting frequencies" and said "there is no cause for concern."
The hacking comes amid several reported incursion attempts and intense shelling in southwestern Belgorod, and as Kyiv says it is preparing a long-expected counteroffensive.
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