Washington DC - The White House said Wednesday it was contacting key US ally Ukraine to learn more about the "objectives" of Kyiv's most serious cross-border incursion into Russian territory in months.

"We're going to reach out to the Ukrainian military to learn more about their objectives," White House Press Secretary Karine Jean-Pierre told reporters when asked about the operation.

Washington supported "common sense" actions by Ukraine to stop attacks by Russian forces, Jean-Pierre added.

President Joe Biden in May allowed Kyiv to use American-supplied weapons against targets just across the Russian border to repel Moscow's push on the Kharkiv region.

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But White House National Security Council spokesman John Kirby said separately that "nothing had changed" about the US policy discouraging broader strikes or attacks inside Russia.

Thousands of civilians on both sides of the border have been evacuated after Ukraine launched the cross-border incursion into Russia's Kursk region, now in its second day.

US State Department spokesman Matthew Miller dismissed Moscow's condemnations of the Ukrainian attack.

"I have seen the statements from the Russian government. It is a little bit rich, them calling it a provocation, given Russia violated Ukraine's territorial integrity and sovereignty," he told a briefing.