Moscow on Thursday claimed that Ukrainians crossed into Russia and opened fire on civilians, an allegation denied 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.
The allegations came as the conflict spilled into the G20 meeting of foreign ministers in New Delhi, with participants unable to agree a joint declaration after objections from Moscow's delegation.
Shortly after Russia reported the alleged incursion, President Vladimir Putin said the attackers were "neo-Nazis and terrorists... who today committed another terrorist attack, penetrated the border area and opened fire on civilians".
However, 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."
AFP could not independently verify the reports.
The FSB security service said that the incident happened in the Klimovsky district of the Bryansk region, which borders Ukraine, and that a "large number of explosives" had been found.
Kremlin spokesman Dmitry Peskov said there had been "an attack by Ukrainian fighters".
Earlier in the day Bryansk regional governor Alexander Bogomaz said "a reconnaissance and sabotage group" had crossed the border near a village called Lyubechane.
Bogomaz said the group had opened fire on a moving car and that one person was killed and a 10-year-old wounded.
"The child has been taken to the hospital, he is receiving all the necessary assistance," Bogomaz said on Telegram.
Russian news agencies, citing sources in law enforcement and the emergency services, said members of the group may have taken hostages.
However, a different account was put forward in two videos on social media that 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.
Bogomaz also said that 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.
The governor of another Russian border region, Kursk, Roman Starovoyt, 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.
Russian officials say regions bordering Ukraine are routinely shelled by Ukrainian forces but the infiltration, if confirmed, would be a rare instance of fighting inside Russia.
In Ukraine, officials said a Russian strike on an apartment block in the southern city of Zaporizhzhia had killed at least three people as search operations continued.
"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," Zelensky added.
Ukraine tensions disrupted the G20 meeting of foreign ministers in India, where the nations couldn't agree a joint declaration after Moscow's objections.
Foreign Minister Sergei Lavrov told the assembled foreign ministers that Western representatives had derailed the meeting, calling it a "farce".
US Secretary of State Antony Blinken and Lavrov spoke briefly at the meeting, in the highest one-to-one contact between Washington and Moscow since Russia's offensive in Ukraine began last year.
Also on the diplomatic front, German Chancellor Olaf Scholz said that Germany and its allies were in talks with Kyiv over future security guarantees in preparation for a 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 Friday.