US President Joe Biden's national security adviser said on Sunday that Russia's advance on Ukraine's Kharkiv "has stalled", after Washington partially lifted restrictions on using US-donated weapons to strike inside Russia.

"The momentum of that operation in Kharkiv has stalled out," Jake Sullivan told the CBS broadcaster.

"Kharkiv is still under threat but Russians have not been able to make material progress on the ground in recent days in that area."

Washington has given the green light for Ukraine to use US weapons to defend its Kharkiv region, on the border with Russia, overcoming previous concerns that authorising such strikes could drag the NATO military alliance into a direct conflict with Russia.

"From the president's perspective, this was common sense," Sullivan said.

"It simply didn't make sense not to allow the Ukrainians to fire across that border, to hit Russian guns and emplacements that were firing at the Ukrainians."

Biden, who is on a visit to France, met Ukrainian President Volodymyr Zelensky in Paris on Friday, reiterating his support for the war-torn country.

Speaking on Saturday, Biden said Russian President Vladimir Putin would "not stop" at Ukraine.

"All of Europe will be threatened. We are not going to let that happen," Biden told journalists alongside French President Emmanuel Macron after talks at the Elysee Palace.

Russian forces made their most significant territorial gains in 18 months during a major ground assault on the Kharkiv region last month, capturing several Ukrainian border villages and forcing thousands from their homes.