Three Ukraine-based Russian paramilitary groups say they have crossed into Russia and are now fighting government troops there.
The Freedom of Russia Legion (FRL) and Siberian Battalion (SB) posted videos purportedly showing their fighters in Russia’s Belgorod and Kursk regions.
The FRL and an exiled Russian politician claimed two villages were now in control of “liberation forces”.
Russia’s defence ministry said the breakthrough attempts were thwarted.
It claimed more than 234 Ukrainian troops had been killed and several tanks had been destroyed.
According to Belgorod’s regional governor, Vyacheslav Gladkov, one member of Russia’s territorial defence forces was killed and 10 civilians were injured.
These numbers have not yet been verified by the BBC.
Ukraine’s military denied any involvement in Tuesday’s cross-border raids. Andriy Yusov, a spokesman for the country’s military intelligence, said the paramilitary groups were “independent organisations” of Russian nationals, and therefore operating “at home”.
In a separate development, Russia said Ukraine had launched 25 drones on targets across Russia, but the attack was thwarted.
However, videos have emerged which appear to show several Russian oil facilities on fire.
In the Ivanovo region, just east of Moscow, an Il-76 military transport plane with eight crew and seven passengers crashed shortly after take-off, Russia’s defence ministry was quoted as saying by Russian state-run news agencies.
The ministry said an engine fire caused the crash. It gave no details of survivors.
Videos have emerged purportedly showing the plane on fire circling in the sky, and later plumes of black smoke from the crash site.
Elsewhere, at least three people were killed and 38 injured on Tuesday night when a Russian missile struck two apartment buildings in the central Ukrainian city of Kryvyi Rih, according to the minister of internal affairs.
Ihor Klymenko said children were among the victims and that the number of deaths may go up as the search and rescue operation is continuing.
Ukrainian President Volodymyr Zelensky said the country would “inflict losses on the Russian state in response – quite rightly”.
A full-scale invasion of Ukraine launched by Russian President Vladimir Putin is now in its third year, with no signs that the biggest war in Europe since World War Two could end soon.
On Tuesday, the FRL posted what it said was a video from the Russian-Ukrainian border.
“Like all our fellow citizens, in the Legion we dream of a Russia freed from Putin’s dictatorship. But we don’t just dream: we make every effort to make these dreams come true. We will take our land away from the regime, centimetre by centimetre,” an armed FRL soldier in the footage is heard saying.
Meanwhile, the SB said “fierce fighting is going on the Russian Federation territory”, publishing a clip purportedly showing its fighters engaging with Russian government forces.
It also condemned Russian presidential elections on 15-17 March, in which Mr Putin is widely expected to be declared the winner.
“Ballots and polling stations in this case are fiction. You can really change your life for the better only with weapons in your hands,” the SB said.
Another Ukraine-based Russian group, the Russian Volunteer Corps (RDK), also published footage of what it said were its fighters engaging with Russian government troops.
“The army of the Kremlin regime lays down its weapons without even starting the battle,” it said.
The videos have not been independently verified.
The border village of Tetkino in the Kursk region appeared to be one of the targets in Tuesday’s raids, with the FRL claiming that “liberating forces” now had full control over the settlement.
The BBC has verified the authenticity of FRL footage depicting a strike on an armoured personnel carrier in Tetkino.
A full-scale invasion of Ukraine launched by Russian President Vladimir Putin is now in its third year, with no signs that the biggest war in Europe since World War Two could end soon.
On Tuesday, the FRL posted what it said was a video from the Russian-Ukrainian border.
“Like all our fellow citizens, in the Legion we dream of a Russia freed from Putin’s dictatorship. But we don’t just dream: we make every effort to make these dreams come true. We will take our land away from the regime, centimetre by centimetre,” an armed FRL soldier in the footage is heard saying.
Meanwhile, the SB said “fierce fighting is going on the Russian Federation territory”, publishing a clip purportedly showing its fighters engaging with Russian government forces.
It also condemned Russian presidential elections on 15-17 March, in which Mr Putin is widely expected to be declared the winner.
“Ballots and polling stations in this case are fiction. You can really change your life for the better only with weapons in your hands,” the SB said.
Another Ukraine-based Russian group, the Russian Volunteer Corps (RDK), also published footage of what it said were its fighters engaging with Russian government troops.
“The army of the Kremlin regime lays down its weapons without even starting the battle,” it said.
The videos have not been independently verified.
The border village of Tetkino in the Kursk region appeared to be one of the targets in Tuesday’s raids, with the FRL claiming that “liberating forces” now had full control over the settlement.
The BBC has verified the authenticity of FRL footage depicting a strike on an armoured personnel carrier in Tetkino.