Kursk, Russia - Thousands of Ukrainian troops are taking part in an incursion aiming to destabilize Russia by showing up its weaknesses, a top official from Ukraine has told AFP as the surprise assault entered its sixth day.

"We are on the offensive. The aim is to stretch the positions of the enemy, to inflict maximum losses and to destabilize the situation in Russia as they are unable to protect their own border," the security official said on condition of anonymity.

The Russian army had said about 1,000 Ukrainian troops were deployed in the cross-border incursion which began on Tuesday and appeared to catch the Kremlin off guard, allowing Ukrainian forces to penetrate Russian defensive lines.

Asked whether the 1,000 figure was right, the official said: "It is a lot more... Thousands".

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After days of official silence, President Volodymyr Zelensky acknowledged the offensive for the first time in his nightly address on Saturday, saying that Kyiv was "pushing the war into the aggressor's territory".

Russia invaded Ukraine in February 2022 and has waged an unrelenting offensive, occupying swathes of eastern and southern Ukraine and subjecting Ukrainian cities to daily missile and drone attacks. After re-capturing large areas in 2022, Ukrainian forces have largely been on the back foot and are increasingly struggling with manpower and arms supplies.

But Ukrainian units stormed across the border Tuesday in what so far has been the largest and most successful such offensive by Kyiv in the conflict.

Its troops have advanced several miles, forcing Russia's army to rush in reserves and extra equipment, though neither side has given precise details on the forces committed.

Russia has evacuated tens of thousands of civilians from the area, and Ukraine has also evacuated thousands of people from the Sumy region across the border.

The operation has "greatly raised our morale, the morale of the Ukrainian army, state and society," the Ukrainian official said, speaking late Saturday after weeks of Russian advances in eastern Ukraine.

"This operation has shown that we can go on the offensive, move forward," the official said. "It seems that the Russians have problems with coordination, preparedness for action."

But the official said there had been little effect so far on fighting in the east.

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"The situation is basically unchanged. Their pressure in the east continues, they are not pulling back troops from the area," he explained, adding only that "the intensity of Russian attacks has gone down a little bit".

The official said Ukrainian troops would respect international humanitarian law while on Russian territory and had no plans to annex areas they currently hold.

"There is no idea of annexation... We are operating in strict accordance with international law," he said, contrasting this with alleged violations by Russian troops in occupied territory.

Asked whether capturing the Kursk nuclear power plant near the border was an aim, he said: "We will see how the Kursk operation will develop".

"We absolutely will not cause problems for nuclear security. This we can guarantee," he said.

The White House said Wednesday it was contacting Ukraine to learn more about the "objectives" of the incursion.

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.

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

Asked whether Western partners had been kept in the dark about Kyiv's offensive, the Ukrainian official said this was "incorrect."

"Judging by how actively Western arms are being used, our Western partners played a part indirectly in the planning," he insisted.

The official said he expected Russia would "in the end" manage to stop Ukrainian forces in Kursk and retaliate with a large-scale missile attack, including "on decision-making centers" in Ukraine.

There has already been more intense bombardment of Ukraine's Sumy region, just across the border from Kursk.

And an overnight missile attack near Kyiv killed a man and his four-year-old son, emergency services said.

Explosions rang out Saturday night in the center and east of Kyiv after Ukraine's air force said two Russian missiles were headed towards the city.