Moscow said on Tuesday it had routed and killed scores of "Ukrainian nationalists" who crossed into Russia from Ukraine after two days of combat, in what appeared to be one of the biggest incursions of its kind of the 15-month-old war.
There was no immediate independent confirmation that the fighting had ended, but the governor of Russia's Belgorod region said the anti-terrorism measures he introduced after Monday's attack had been lifted.
And one of two groups claiming to be behind the raid said in a post on social media: "One day we will return to stay."
The fighting forced Russia to evacuate towns along the border with northeast Ukraine. Russia has blamed Ukraine for the attack, which Kyiv has denied. The two groups that claimed responsibility describe themselves as Russian armed dissidents.
The Russian military said it had killed more than 70 Ukrainian nationalists and destroyed four armoured vehicles. There was no independent confirmation of those losses.
Russian forces had surrounded the enemy fighters and defeated them with "air strikes, artillery fire and active action by border units", the defence ministry said.
"The remnants of the nationalists were pushed back to Ukrainian territory, where they continued to be hit by gunfire until they were completely eliminated," it added.
Regional governor Vyacheslav Gladkov said one elderly woman had died during the evacuation. On Monday, he said at least eight people had been wounded, several buildings damaged and many residents had left.
The two groups who claimed responsibility, the Freedom of Russia Legion and the Russian Volunteer Corps (RVC), both say they comprise armed Russian fighters seeking to overthrow President Vladimir Putin.
The Legion says it is recognised by Ukraine and its members have fought there against Russian forces. The RVC has claimed responsibility for previous attacks inside Russia, including a cross-border raid in the neighbouring Bryansk region in March.
"Good morning everybody, except Putin's henchmen. We have met the dawn on liberated territory, and are moving further on," the Legion said on Telegram.
"Once again, the myth that the citizens of the Russian Federation are safe and the Russian Federation is strong has been destroyed," it said in a later post.
The RVC said: "One day we will come to stay. Meanwhile, the partisan movement is not bound by the framework of traditional combat operations."
It wasn't us, says Kyiv
Mark Galeotti, head of the London-based Mayak Intelligence consultancy, said the militant groups covered a variety of political perspectives united by wanting to see Putin's downfall.
"But at the same time, we have to realise that these are not independent forces... They are controlled by Ukrainian military intelligence. They rely on the Ukrainians for weapons and support."
Kyiv publicly denied blame for the raid, though some of its denials were pitched with apparent irony, to mimic past Russian denials of a role in separatist movements in Ukraine.
Kyiv "has nothing to do with it", tweeted Ukrainian presidential adviser Mykhailo Podolyak. "As you know, tanks are sold at any Russian military store, and underground guerrilla groups are composed of Russian citizens."
Moscow, which portrays its invasion of Ukraine last year as a response to a security threat from Kyiv, said the attackers were Ukrainian saboteurs, seeking to deflect attention from Russia's capture of the city of Bakhmut three days ago, after the bloodiest land battle in Europe since World War Two.
"This once again confirms that Ukrainian militants are continuing their activities against our country. This requires a great deal of effort from us, and these efforts are continuing," Kremlin spokesman Dmitry Peskov said.
Asked about reports that the attackers were ethnic Russians, he said: "They are Ukrainian fighters from Ukraine. There are many ethnic Russians living in Ukraine. But they are still Ukrainian militants."
The RVC released video of a fighter with what it said was a captured armoured vehicle, putting a sticker with the group's logo over the "Z" symbol used to identify Russian forces.
Other videos posted on Russian and Ukrainian social media channels showed images of what were described as captured Russian servicemen and their identity documents.
Mash, a Russian news channel on Telegram, said drones had struck the roof of the Russian FSB security service building in Belgorod city overnight, nearly 80km from the district where the raid took place. It posted a picture of emergency vehicles outside the building.
Inside Ukraine, Russian forces are celebrating their first notable victory in 10 months with the capture of Bakhmut, where thousands of troops died in months of fighting both sides call a meatgrinder. Kyiv says its forces have been making their own gains on the outskirts of Bakhmut to the north and outh.
Nato Secretary-General Jens Stoltenberg said on Tuesday that training Ukrainian pilots in flying US-built F-16 fighter jets, as endorsed by US President Joe Biden, did not make Nato a party to the conflict.
Former Russian president Dmitry Medvedev said that the more destructive the weapons that Ukraine receives from the West, the higher the risk of "nuclear apocalypse", the state-owned news agency RIA reported.