Ukraine has called Moscow's claims that its fighters crossed into Russia and killed two civilians a "deliberate provocation".
If confirmed, the alleged incursion would be a rare instance of fighting inside Russian territory, despite its claims that regions on its border are routinely shelled by Ukrainian forces.
The "Ukrainian nationalists" had later been pushed back over the border and hit with a "massive artillery strike", Russia's FSB security service said.
President Vladimir Putin said the attackers, who he called "neo-Nazis and terrorists", had "penetrated the border area and opened fire on civilians".
But Ukrainian presidential adviser Mykhaylo Podolyak quickly dismissed Moscow's claims.
"The story about a sabotage group in Russia is a classic deliberate provocation," Mr Podolyak said.
"Russia wants to scare its people to justify the attack on another country and the growing poverty after the year of war."
One year of the Russia-Ukraine war - in pictures
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February 24 will be a year since Russia started the Ukraine war. The National picks out the most powerful images from the conflict. AFP -
A member of Ukraine's 79th Air Assault Brigade fires a rocket-propelled grenade at Russian positions near Marinka in February. Reuters -
Ukrainian President Volodymyr Zelenskyy addresses MPs in Westminster Hall, London, in February 2023. Getty Images -
Destroyed buildings 32km west of the front lines in Donetsk in January. Getty Images -
An anti-aircraft gun in January fires at Russian positions near Bakhmut, Donetsk. Reuters -
Destruction in the village of Bohorodychne, Donetsk. AFP -
A Ukrainian artilleryman discards an empty shell on the outskirts of Bakhmut, eastern Ukraine, in December 2022. AFP -
Children receive presents from a Ukrainian soldier dressed as Santa on Christmas Eve in Sloviansk. Getty Images -
More than 1,000 missiles and rockets fired by Russian forces collected for cataloguing in Kharkiv in December 2022. Getty Images -
The Metro provides shelter as Russia launches another missile attack on Kyiv, Ukraine's capital, in December 2022. Getty Images -
Children at a PE class in Kyiv after Russia abandoned its attempt to seize the capital in November 2022. Getty Images -
A sniper searches for Russian positions on the bank of the Dnipro river in Kherson in November 2022. Getty Images -
Graffiti by Banksy on a wall among the debris in Borodyanka in November 2022. Getty Images -
Ukrainian flags flutter around graves in a cemetery for soldiers killed in action in Kharkiv in October 2022. Getty Images -
Parts of a drone, which Ukrainian authorities said was Iranian-made, after a Russian strike in Kyiv in October 2022. Reuters -
An elderly woman is helped across a damaged bridge in Bakhmut in October 2022. Getty Images -
Fuel tanks ablaze on damaged sections of the Kerch bridge in Crimea, in October 2022. Reuters -
A destroyed bridge makes crossing the Donets river difficult, in Staryi Saltiv, east of Kharkiv, in September 2022. AFP -
Firefighters at a thermal power plant in Kharkiv damaged by a Russian missile strike in September 2022. Reuters -
Ukrainian soldier Oleksandr with his daughter Nikole at Lviv railway station in August 2022. Getty Images -
Ukrainian President Volodymyr Zelenskyy and then-British prime minister Boris Johnson read a plaque in Kyiv in August 2022 dedicated to the latter for his support. Getty Images -
Destroyed Russian military equipment on Khreshchatyk street in Kyiv. The materiel was turned into an open-air military museum ahead of Ukraine's Independence Day on August 24. AFP -
Shakhtar Donetsk v Metalist Kharkiv kicks off the Ukrainian Premier League season in August 2022 amid fears of bomb and missile alerts. EPA -
Ukrainian servicemen fire an American-made 155mm M777 howitzer in July 2022 in the Kharkiv area. EPA -
A bomb crater on the Antonovsky bridge across the Dnipro river in Kherson, July 2022. AFP -
Maksym and Andrii with plastic guns at a 'checkpoint' they set up while playing in Kharkiv, July 2022. AP -
Ukrainian troops on Snake Island in June 2022. Reuters -
A woman evacuated from an area of conflict in June 2022 contemplates what the next move might be. AP -
Romanian President Klaus Iohannis, Italian Prime Minister Mario Draghi, Ukrainian President Volodymyr Zelenskyy, French President Emmanuel Macron and German Chancellor Olaf Scholz in Kyiv in June 2022. Getty Images -
Graves in Irpin cemetery, May 2022. Getty Images -
A Ukrainian soldier trapped within the besieged Azovstal Iron and Steel Works complex in Mariupol in May 2022. Reuters -
The wreckage of a Russian helicopter in a bomb-cratered field in Biskvitne, May 2022. Getty Images -
A Ukrainian army officer inspects a grain warehouse shelled by Russian forces in May 2022 near Novovorontsovka, Kherson. Getty Images -
A boy from Mariupol arriving at an evacuation point in Zaporizhzhia in May 2022. Getty Images -
A Russian serviceman on guard outside Zaporizhzhia nuclear power station in May 2022. AFP -
Oksana searches for salvageable items on the destroyed second floor of her home in Hostomel, April 2022. Getty Images -
A floral memorial wall in Lviv for Ukrainian civilians killed during the Russian invasion, April 2022. Getty Images -
People fleeing Lviv, eastern Ukraine, in April 2022, wait for a bus that will take them to Poland. Getty Images -
A Russian soldier patrols a bombed Mariupol theatre in April 2022, as Moscow intensified its campaign to take the strategic port city. AFP -
A Ukrainian celebrates success in Hostomel in April 2022. Getty Images -
Julia Palovskaya reads to children during an air raid drill in the basement shelter at a preschool in Lviv, April 2022. Getty Images -
Volodymyr Zelenskyy in Bucha in April 2022, where hundreds of bodies were found in the street and it was claimed the Russian leadership was responsible for killing civilians. AFP -
Oleh Smolin, 23, who suffered leg injuries from Russian shelling in April 2022, in hospital in Chuhuiv. Getty Images -
Fleeing refugees arrive at the border train station of Zahony, Hungary, in March 2022. Getty Images -
A father says goodbye to his daughter on an evacuation train about to leave Odesa in March 2022. AFP -
Ukrainians under a destroyed bridge as they try to cross the Irpin river on the outskirts of Kyiv in March 2022. AP -
People cram into Kyiv station to catch trains to Poland or to western parts of Ukraine, shortly after the initial invasion in February 2022. Getty Images -
A demonstration in support of Ukraine in Trafalgar Square, London, February 2022 . Getty Images -
Russian army vehicles in Armyansk, Crimea, in February 2022. AFP -
Volodymyr Zelenskyy in Kyiv on February 25, 2022, in a video on Facebook. He said 'we are all here', shortly after the Russian invasion began. AFP -
A residential building damaged by a missile strike in Kyiv in February 2022. Getty Images -
A metro station in Kyiv in February 2022, crowded with people trying to escape the invasion. AFP -
A police officer addresses people gathered to protest against the invasion of Ukraine, in central Saint Petersburg, Russia, February 2022. AFP -
A protester in support of Ukraine, in Berlin, Germany, in February 2022. Getty Images -
Ukrainian soldiers prepare to repel an attack in Ukraine's Lugansk region on February 24, 2022. AFP -
Volodymyr Zelenskyy in Kyiv on February 24, 2022, after Russia launched a full-scale invasion. AFP -
A mass exodus from Kyiv after pre-offensive missile strikes by Russian armed forces on February 24, 2022. Getty Images -
Security personnel inspect the remains of a shell in Kyiv on February 24, 2022, soon after Russian President Vladimir Putin announced a military operation in Ukraine. AFP -
CCTV footage shows Russian military equipment crossing a Crimea border checkpoint on February 24, 2022. AFP -
Russian President Vladimir Putin in the Kremlin early on February 24, 2022, when he announced a 'military operation' in Ukraine. AFP
AFP could not independently verify the reports.
FSB said the incident happened in the Klimovsky district of the Bryansk region, which borders Ukraine, and that a "large number of explosives" had been found.
Earlier in the day, Bryansk regional Governor Alexander Bogomaz said "a reconnaissance and sabotage group" had crossed the border near the village of Lyubechane.
Mr Bogomaz said that two people were killed and a child wounded in the attacks.
He said the boy had been taken to hospital and had a bullet removed during surgery.
But a different account was put forward in two videos on social media, which showed four men in military uniform claiming to be from a Russian volunteer group in the Ukrainian army.
Russia and Ukraine conflict latest - in pictures
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A tank, seen left, fires a round in Soledar, a town in the Donetsk region of eastern Ukraine. Reuters -
Tank fire in Soledar, Donetsk. Reuters -
Firefighters work to put out a blaze at a Kharkiv fireworks storage site after it was struck by a Russian missile. Getty -
Col Gen Oleksandr Syrskyi, commander of Ukraine's ground forces, visits his troops on the frontline in Soledar, Donetsk. Reuters -
A Ukrainian flag attached to a tank flutters in the wind in Bakhmut. Reuters -
A specialist from an emergency crew works on a residential building in Donetsk that was damaged in recent shelling. Reuters -
A missile fragment left by shelling in Russian-controlled Donetsk. AP -
Residents remove debris and carry their belongings out of a building destroyed by recent shelling in Donetsk, Russian-controlled Ukraine. Reuters -
Ukrainian forces fire an anti-aircraft weapon as Russia's attack on the frontline city of Bakhmut continues. Reuters -
A car drives past a destroyed building purported to have been used as temporary accommodation for Russian soldiers, dozens of whom were killed in a Ukrainian missile strike in Makiivka, Russian-controlled Ukraine. Reuters -
The site of a temporary barracks for Russian soldiers in Makiivka, which was destroyed in a Ukrainian missile attack. Reuters -
A Ukrainian serviceman carries his injured comrade from the battlefield to a hospital in the Donetsk region. AP -
Smoke rises after shelling in Soledar, the site of heavy battles with Russian forces in the Donetsk region. AP
The men said they were in Russia and made statements against the Kremlin, denying reports that they had taken hostages or killed anyone.
Mr 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 Bryansk.
Roman Starovoyt, Governor of another Russian border region, said Ukrainian shelling on the village of Tetkino killed one person and injured another.
Mr Starovoyt said the shelling damaged three houses and cut power in the village.
In Ukraine, officials said a Russian strike on an apartment block in the southern city of Zaporizhzhia had killed at least three people.
"The terrorist state wants to turn every day for our people into a day of terror," Ukrainian President Volodymyr Zelenskyy 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."
Drones and weapons supplied to Ukraine - in pictures
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Turkeysold its Bayraktar TB2 armed drones to Ukraine. They can fly at an altitude of 7,500 metres and swoop down to attack targets. AFP -
The US also gave 700 of its Switchblade kamikaze drones. AP -
Cheap commercial drones like the DJI Mavic series have been modified in Ukraine. AFP -
Germany will follow the US in providing a Patriot missile defence system, pictured above, to Ukraine. Reuters -
FIM-92 Stinger rockets have been donated to help Ukrainian infantry engage aircraft and drones. The shoulder-launched missiles can shoot down aircraft. Photo: US Army -
Germany donated 25 Flakpanzer Gepard all-weather-capable self-propelled anti-aircraft gun. AFP -
The High-Mobility Artillery Rocket System, or Himars, can simultaneously launch several precision-guided missiles. The US has given Ukraine projectiles with a range of about 130 kilometres. EPA -
M777 howitzers and about 300,000 shells have been donated to give Ukraine an accurate artillery platform with a range of 50 kilometres. EPA -
Ukraine has been sent at least 5,000 of the anti-tank weapons known as NLAWs. These shoulder-launched rockets have proved deadly in the field. PA -
Ukrainian troops have also received thousands of Javelin anti-tank missiles. Bloomberg -
Poland and the Czech Republic sent Russian-made T72 tanks, which Ukraine has used for decades, to ease integration and cut down training time. EPA -
France as announced its plan to give AMX-10 RC “scout tanks” to Ukraine. "This is the first time that western-made armoured vehicles are being delivered in support of the Ukrainian army," a French official said. AFP -
Shortly after the French, the US said it would send Bradley fighting vehicles to provide "a level of firepower and armour that would bring advantages on the battlefield”. Reuters -
The UK sent their phased-out Saxon armoured vehicles. They found new life protecting infantry units in transit and dealing with tough off-road conditions. Getty Images -
Denmark has supplied Harpoon anti-ship launchers to help Ukraine defend its coasts. AFP -
The US sent 20 Soviet and Russian made Mi-17 helicopters to Ukraine that had initially been bought for the Afghan government in 2010. AP -
Germany has also supplied its latest version of the IRIS-T air defence system designed to shoot down missiles at altitudes up to 20 kilometres. Getty Images -
Ukraine has also been given thousands of small arms, bullet proof vests, medical kits, litres of fuel, granades and other weapons systems. Reuters
Ukraine tension disrupted the G20 meeting in India, with Russian Foreign Minister Sergey Lavrov telling the assembled delegates that western representatives had derailed the meeting, calling it a "farce".
US Secretary of State Antony Blinken said he had told Mr Lavrov to "end this war of aggression, engage in meaningful diplomacy".
Also on the diplomatic front, German Chancellor Olaf Scholz said that Berlin 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," he told the German Parliament.
"Such security guarantees, however, come with the presumption that Ukraine successfully defends itself in this war."
Mr Scholz will travel to the US for talks with President Joe Biden on Friday.
