MOSCOW, March 2 (AFP) - Moscow on Thursday (Mar 2) 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.