The Kremlin said a purported radio address by President Vladimir Putin heard Monday on Russian stations in regions bordering Ukraine was fake and the result of a hack, Russian news agencies reported.

The state-owned news agency RIA said a number of radio stations carried the hoax address.

"All of these messages are an utter fake," it cited Kremlin spokesman Dmitry Peskov as saying.

Independent Russian media reported that the announcement had told residents of the Rostov, Belgorod, and Voronezh regions, all of which adjoin Ukraine, that Kyiv's forces had crossed the border with Russia.

They cited the address as saying, wrongly, that martial law had been declared in border regions and a nationwide military mobilization had begun for Russia's war with Ukraine, and that residents should evacuate deeper into Russia.

Kyiv denies sending any troops into Russian territory, and said the sporadic ground incursions that have occurred in the last three months, for which Moscow blames Ukraine, have been the work of Russian partisans.

In a statement posted on Telegram, the Voronezh regional government confirmed that a hack had taken place, and said local radio stations were under the control of law enforcement agencies and local authorities.