Moscow on Thursday claimed that Ukrainians had crossed into southern Russia and killed two civilians, an allegation dismissed by Kyiv as a "deliberate provocation."
Russia says its regions bordering Ukraine are routinely shelled by Ukrainian forces, but the alleged incursion, if confirmed, would be a rare instance of fighting inside its territory.
Russia's FSB security service said in a statement that the "Ukrainian nationalists" had later been pushed back over the border and targeted with a "massive artillery strike."
It comes as Ukraine orders the mandatory evacuation of vulnerable residents from the frontline city of Kupiansk and adjacent northeastern territories, with fears mounting that Russia will retake the key city and rail hub.
The conflict has also spilled into the G20 meeting of foreign ministers in New Delhi, with US Secretary of State Antony Blinken saying he had urged Russia's top diplomat Sergei Lavrov to end the military campaign in Ukraine.
President Vladimir Putin denounced the attackers accused of the incursion as "neo-Nazis and terrorists," saying they had "penetrated the border area and opened fire on civilians."
Ukrainian presidential advisor Mykhaylo Podolyak quickly dismissed Moscow's claims.
"The story about (a) sabotage group in Russia is a classic deliberate provocation," he said. "Russia wants to scare its people to justify the attack on another country and the growing poverty after the year of war."
The FSB said the incident had happened in the Klimovsky district of the Bryansk region, which borders Ukraine, and that a "large number of explosives" had been found.
AFP could not independently verify the reports.
'Sabotage group'
Earlier in the day, Alexander Bogomaz, governor of the Russian region of Bryansk, said "a reconnaissance and sabotage group" had crossed the border near a village called Lyubechane.
Bogomaz said two people were killed and a child wounded in the attacks.
He said the boy was taken to hospital and had a bullet removed during surgery.
However, a different account was put forward in two videos on social media. They showed four men in military uniform claiming to be from a Russian volunteer group in the Ukrainian army.
The men said they were in Russia and made statements against the Russian government, denying reports that they had taken hostages or killed anyone.
Governor Bogomaz also said a Ukrainian drone had attacked the village of Sushany, leaving a residential home in flames, and that mortar fire had damaged two homes in Lomakovka, also in the region of Bryansk.
Roman Starovoyt, the governor of another Russian border region, said Ukrainian shelling on the village of Tetkino had left one dead and one injured.
He said the shelling damaged three houses and cut power in the village.
'Evil will not reign'
Ukraine's evacuation order in the northeast came as Kharkiv regional governor Oleg Synegubov said Russia had "shelled" several settlements in the area, including Kupiansk.
Russian troops retreated from key cities in the region in September, but locals fear Kupiansk could be recaptured.
"Mandatory evacuation of families with children and residents with limited mobility began in Kupiansk community," the Kharkiv regional military administration said on its website.
"The decision was made... taking into account the unstable security situation due to constant shelling of the territory of the community by Russian troops," it added.
Some 300 kilometres (185 miles) further south, a Russian strike on an apartment block in the southern city of Zaporizhzhia killed at least three people, Ukrainian officials said.
"The terrorist state wants to turn every day for our people into a day of terror," Ukrainian President Volodymyr Zelensky said.
"But evil will not reign in our land. We will drive all the occupiers out and they will definitely be held accountable for everything," he added.
G20 'farce'
Ukraine tensions disrupted the G20 meeting in India, with Lavrov telling the assembled foreign ministers that Western representatives had derailed the meeting, calling it a "farce."
His US counterpart Blinken said he had told Lavrov to "end this war of aggression, engage in meaningful diplomacy."
Also on the diplomatic front, German Chancellor Olaf Scholz said Germany and its allies were in talks with Kyiv over future security guarantees in preparation for sustainable peace for Ukraine.
"We are speaking with Kyiv and other partners over future security guarantees for Ukraine," Scholz said in a speech to the German parliament.
"Such security guarantees, however, come with the presumption that Ukraine successfully defends itself in this war," said Scholz, who will travel to the United States for talks with President Joe Biden on Friday.
The White House announced that Biden would also host European Commission chief Ursula von der Leyen for talks in Washington next week.
