Russian officials have declared the situation in the Kursk region a “federal level” emergency, four days after hundreds of Ukrainian troops poured over the border in what appears to be Kyiv’s biggest attack on Russian soil since the war began.

Kursk acting governor Alexei Smirnov said on Telegram: “The operational situation in the Kursk region remains difficult.”

Social services and civic associations are providing assistance to people forced to flee their homes by the fighting, he said. The last Russian figure for evacuations in Kursk was 3,000.

Little reliable information about the surprise Ukrainian operation has emerged, and its strategic aims are unclear.

Ukrainian officials have refused to comment specifically about the incursion, which is taking place about 320 miles south-west of Moscow.

Fighting has broken out in the Kursk region (Governor of Kursk region telegram channel via AP)

But a top adviser to Ukraine President Volodymyr Zelenskyy said on Thursday that border region attacks will cause Russia to “start to realise that the war is slowly creeping inside of Russian territory”.

Myhailo Podolyak also suggested that the operation would improve Kyiv’s hand in the event of negotiations with Moscow.

The assault came as the Ukrainian army toils to hold at bay an intense Russian push at places on the front line in eastern Ukraine, especially in the Donetsk region.

Russian President Vladimir Putin has made clear he wants to capture the parts of Donetsk that the Kremlin’s forces do not already occupy.

Russia declares federal level emergencies when there are more than 500 victims or damage exceeds 500 million roubles (about £4.7 million).

The Institute for the Study of War, a Washington-based think tank, says Ukrainian forces have pressed on with their “rapid advances” deeper into the Kursk region, reportedly going up to 20 miles beyond the border.

The Ukrainian forces have launched an assault over the Russian border (Oleg Petrasiuk/Ukrainian 24th Mechanised Brigade via AP)

“The lack of a coherent Russian response to the Ukrainian incursion into Kursk … and the reported rate of Ukrainian advance indicates that Ukrainian forces were able to achieve operational surprise,” the Washington-based ISW said late Thursday.

A Russian defence ministry said only that the military “continues to repel the attempted invasion” and is responding with air strikes, artillery and troops on the ground.

Ukraine has also kept up its strategy of hitting rear areas with long-range drones, targeting military sites, oil refineries and other infrastructure.

Ukrainian drones attacked Russia’s Lipetsk region, which is about 180 miles from the Ukraine border, during Thursday night, authorities said.

The regional emergencies ministry in Lipetsk said there was a fire at a military airfield where fighter planes including MiG-29s and Su-34s reportedly are based.

Lipetsk governor Igor Artamonov said that unspecified electrical infrastructure was damaged and nine people were wounded in the attack.

The Russian defence ministry said that 75 Ukrainian drones were shot down during the night, 19 of them over Lipetsk.