Russia's army on Sunday appeared to acknowledge Ukraine had pierced deep into its territory in the six-day offensive, saying it had hit Ukrainian troops and equipment in places around 30 kilometres (20 miles) from the border.

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

The shock offensive appeared to catch the Kremlin off guard.

The Ukrainian official also said Russia's claims that it had deployed 1,000 troops were a major underestimation of the forces Kyiv has committed to the operation.

"It is a lot more... Thousands".

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 campaign, occupying swathes of the east and south and subjecting Ukrainian cities to daily missile and drone attacks.

After re-capturing large areas in 2022, Kyiv has largely been on the back foot, increasingly struggling with manpower and arms supplies.

The cross-border incursion into Russia's western Kursk region has been the largest and most successful such offensive by Kyiv so far.

Russia's army has been forced to rush in reserves and extra equipment, and evacuate at least 76,000 civilians from border areas.

The defence ministry on Sunday said it had "foiled attempts" by Ukrainian troops, using armoured vehicles "to break through deep into Russian territory."

But in an apparent sign of how far some Ukrainian units have managed to advance, it said it had hit enemy units near the villages of Tolpino and Obshchy Kolodez, which are around 25 km and 30 km from the Russia-Ukraine border.

- Morale boost for Ukraine -

AFP journalists in Ukraine's Sumy region, from where Ukraine launched the incursion, saw dozens of armoured vehicles daubed with a white triangle on Sunday -- the insignia apparently being used to identify Ukrainian military hardware being used in the attack.

Neither side has given precise details on the extent of their deployments to the new conflict zone.

Ukrainian authorities in the Sumy region have also announced plans to evacuate some 20,000 people close to the Russian border, which has come under fire in response.

At an evacuation centre in the regional capital of Sumy, retired metal worker Mykola, who had fled his village of Khotyn some 26 kilometres (16 miles) from the Russian border, said the offensive had given him a morale boost.

"Let's let them find out what it's like. They don't understand what war is. Let them have a taste of it," the 70-year-old told AFP, despite being forced to leave his home.

Analysts said Kyiv may have launched the assault in a bid to relieve pressure on its troops in other parts of the sprawling front line.

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

"Their pressure in the east continues, they are not pulling back troops from the area," he said, adding that "the intensity of Russian attacks has gone down a little bit".

Ukrainian troops would respect international humanitarian law while on Russian territory and had no plans to annex areas they currently hold, he added.

"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.

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 centres" in Ukraine.

Russia has vowed a "tough" response to the incursion and a Ukrainian missile strike on a residential building in Kursk that it said injured 15.

An overnight missile attack near the Ukrainian capital Kyiv killed a man and his four-year-old son, emergency services said.