Ukrainian authorities evacuated thousands of civilians Sunday as Russian forces kept up constant attacks on the key border town of Kharkiv.

The surprise Russian attack across Ukraine's northeastern border began Friday, with Moscow's troops making small advances in an area from where they had been pushed back nearly two years ago.

"In total, 4,073 people have been evacuated," Kharkiv regional Gov. Oleg Synegubov wrote on social media, a day after Russian forces claimed the capture of five villages in the region.

Synegubov said a 63-year-old man was killed by artillery fire in the village of Glyboke. and a 38-year-old man was wounded in Vovchansk, a border town that had some 3,000 residents before the current offensive.

"The city is constantly under fire," said Oleksiy Kharkivsky, a senior police officer from Vovchansk helping to coordinate the evacuations.

"Everything in the city is being destroyed ... You hear constant explosions, artillery, mortars. The enemy is hitting the city with everything they have," he said, speaking at an evacuation point in a village near Vovchansk.

Evac teams under fire

Kharkivsky said one person who was trapped under rubble had died overnight and "several people were killed by shelling" on Saturday.

He estimated that around 1,500 people had been evacuated or fled Vovchansk since Friday and said there had been 32 drone strikes on the town over the past 24 hours.

He said evacuation teams had come under fire "many times."

On Saturday, AFP saw groups of people fleeing the border area arriving in vans and cars loaded with bags at a reception center for evacuees near Kharkiv.

Evacuees – most of them elderly – received food and medical assistance and could sleep in bunk beds.

One 61-year-old woman, Lyubov Nikolaieva, told AFP she had fled the border village of Lyptsi along with her 81-year-old mother.

"There is constant incoming fire: those guided aerial bombs and mortar shells whistling overhead. It became very scary," she said.

President Volodymyr Zelenskyy said Saturday that Ukrainian troops had been carrying out counterattacks in border villages in Kharkiv region.

"Disrupting Russian offensive plans is now our number one task," he said.

Troops must "return the initiative to Ukraine," the president insisted, again urging allies to speed up arms deliveries.

Ukrainian officials had warned for weeks that Moscow might try to attack its northeastern border regions, pressing its advantage as Ukraine struggles with delays in Western aid and manpower shortages.