In one of the most striking battles of the three-year-old Ukraine war, Ukrainian forces smashed their way across Russia's western border in Kursk in August, marking the biggest attack on sovereign Russian territory since the Nazi invasion of 1941.
But a lightning offensive in March has reduced the area under Ukrainian control to about 110sq km, down from the more than 1368sq km claimed by Kyiv in 2024, according to open source maps.
Yuri Podolyaka, one of the most influential pro-Russian military bloggers, said Russia had pushed back Ukrainian forces to the border in some areas, though intense battles were under way and that Ukrainian forces were fighting back as they retreated.
Battlefield maps from Ukraine and Russia showed two joined pockets of Ukrainian forces on the Russian side of the border in Kursk.
Russia said it was clearing large numbers of mines in the area.
After a public appeal by US President Donald Trump last week to spare "surrounded" Ukrainian troops, Putin said on Friday that Russia would guarantee the lives of Ukrainian troops in the region if they surrendered.
President Volodymyr Zelenskiy said on Saturday his troops were not surrounded but sounded the alarm over what he said could be a new Russian attack on Ukraine's northeast Sumy region, which borders Kursk.
The influential Two Majors pro-Russian military blogger said the battlefield gains of Russian forces had allowed Russia to threaten Sumy, but cautioned that Ukrainian forces had been bolstering defences there for some time.
Putin has accused Ukrainian troops of carrying out crimes against civilians in Kursk, something Kyiv denies.
Ukraine says as many as 11,000 North Korean troops are fighting with Russia in Kursk, though Russia and North Korea have refused to give any details on North Korean troops there.
The fierce battle for the Kursk region has framed efforts by Trump to end what he says is a "bloodbath" war that could escalate into World War III.
Russia's invasion of Ukraine in February 2022 has left hundreds of thousands of people dead and injured, displaced millions, reduced towns to rubble and triggered the sharpest confrontation for decades between Moscow and the West.
The US agreed on Tuesday to resume military aid and intelligence sharing with Ukraine after Kyiv said it was ready to support Washington's proposal for a 30-day ceasefire.
Putin said on Thursday Russia supported the truce proposal in principle, but that fighting could not be paused until crucial conditions were worked out or clarified.
Putin has repeatedly said that he is ready to talk about peace although Ukraine would have to declare it would not seek NATO membership and Russia would keep all of the land that it claims in Ukraine, including some it does not control.
Russia has paid a heavy price for the invasion.
US intelligence estimates say more than 100,000 Russian troops have been killed or injured, according to a 2023 assessment, while the economy has been heavily distorted by record defence spending and the toughest Western sanctions ever imposed.
Ukraine has also had more than 100,000 troops killed or injured, according to leaked US intelligence estimates.
Its economy has been shattered.
One-fifth of its territory is under Russian control, and Kyiv has been unable to defeat Russia's forces despite receiving more than $US260 billion ($A411 billion) in Western aid.
Neither side discloses current death toll figures for the war.
