Ukraine said its biggest cross-border assault of the war had captured 1,000 square kilometres (386 square miles) of Russia's Kursk region and that Russian President Vladimir Putin would have to be forced into making peace.

With Russia still struggling to repel the surprise assault a week after it began, Ukraine's top commander Oleksandr Syrskyi briefed President Volodymyr Zelenskiy by video link and said the advance into Russian territory was ongoing.

"We continue to conduct an offensive operation in the Kursk region. Currently, we control about 1,000 square kilometres of the territory of the Russian Federation," he said in a video published on Zelenskiy's Telegram account.

He provided scant other detail, continuing Kyiv's strategy of silence that contrasts starkly with last year's counteroffensive that was known about for months in advance and which foundered on Russian defensive lines.

Syrskyi spoke a few hours after Alexei Smirnov, Russia's acting regional governor of Kursk, estimated that Kyiv's forces had taken control of 28 settlements in an incursion that was about 12 km deep and 40 km wide.

Though less than half Syrkyi's estimate of the Ukrainian gains, Smirnov's remarks were a striking public admission of a major Russian setback more than 29 months since it launched a full-scale invasion of its smaller neighbour.

Putin has described the cross-border attack as a "major provocation" and said it was aimed at improving Kyiv's negotiating position.

Zelenskiy told Ukrainians in his nightly address that the operation was a matter of Ukrainian security and the Kursk region had been used by Russia to launch many strikes against Ukraine.

He said Ukraine's northeastern Sumy region, which lies across the border from Kursk region, had been struck by Russia almost 2,100 times since June 1.

"Russia must be forced to make peace if Putin wants to fight so badly," Zelenskiy said.

DIVERT TROOPS

The Ukrainian attack comes after months of slow but steady advances by Russian forces in the east that has forced Ukraine's troops onto the back foot as they try to withstand Russia's heavy use of gliding bombs and assault troops.

Former Ukrainian defence minister Andriy Zagorodnyuk told Reuters the Kursk operation looked like it aimed to distract Russian forces and its leadership from the eastern fronts.

"The apparent goal is to create a problem area for Russia, which will distract its forces and its leadership's attention and resources from where they're trying to succeed right now," he said by phone.

Visiting Kyiv on Monday, U.S. Republican Senator Lindsey Graham urged the U.S. presidential administration to provide Ukraine with the weapons it needs.

"What do I think about Kursk? Bold, brilliant, beautiful. Keep it up," he told reporters.

Putin has said Ukraine had received help from its "Western masters" and vowed that "the enemy will certainly receive a worthy response".