Ukraine - Russia said Sunday it had captured four more villages in Ukraine's Kharkiv region, as thousands of residents were evacuated from the offensive in an area where Russian troops had been pushed back in 2022.

President Volodymyr Zelensky said that "fierce fighting" was underway, and governor Oleg Synegubov said "all areas" of the regional border with Russia were now "under enemy fire almost around the clock."

Across the border in the Russian city of Belgorod, emergency services said eight people were killed when a residential building was hit by a Ukrainian missile after it was intercepted by air defenses.

In Ukraine, local prosecutors said four civilians had been killed in the Kharkiv region in the ground Russian offensive, which was launched on Friday.

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The Ukrainian army's top commander said that although the situation was "complicated," his forces were managing to hold back further Russian advances.

But Russia's defense ministry said its forces had "advanced deeply into the enemy defenses" as it announced the latest territorial gains, a day after claiming the capture of five villages in the Kharkiv region.

At an evacuation point near the front line in the Kharkiv region, AFP reporters on Sunday saw groups of people evacuated from around the border town of Vovchansk, most of them elderly and disoriented.

"We weren't going to leave. Home is home," said 72-year-old Lyuda Zelenskaya, hugging a trembling cat named Zhora.

Liuba Konovalova (70) said she had endured a "really terrifying" night before her evacuation.

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Volunteers assisted evacuees to a few wooden benches where they registered and received food before being evacuated towards Kharkiv, the regional capital.

Emergency services said more than 4,500 people had been evacuated from the Kharkiv region.

"Defensive battles and fierce fighting continue on a large part of our border," Zelensky said in his evening address.

"There are villages that have actually turned from a 'gray zone' into a combat zone, and the occupier is trying to gain a foothold in some of them or simply use them for further advancement," he said.

A "gray zone" is territory not fully controlled by either side.

Zelensky said the situation was "extremely difficult" around Vovchansk, adding: "Our task is obvious: we need to inflict as many losses as possible on the occupier."

Speaking at an evacuation point near Vovchansk, Oleksiy Kharkivsky, a senior police officer helping to coordinate evacuations, said the area was "constantly under fire."

"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.

Evacuation teams had come under fire "many times," he added. Officials estimated there were still around 500 civilians left in Vovchansk as Russian troops closed in.

Volodymyr Tymoshko, head of police in the Kharkiv region, said the town was being attacked on three sides, and Russian troops were on the outskirts.

"Despite active fighting, the police are still taking out people who live some 300, 500 meters from the contact line at the moment," he told AFP at the evacuation point.

The Ukrainian army said its defenses were holding.

"Russian occupants' attempts to break through our defense have been stopped," Ukraine's commander-in-chief, Oleksandr Syrsky, said on social media.

But the situation in the Kharkiv region had "deteriorated significantly," he added.

Ukrainian forces "are doing everything they can to hold their defensive lines and positions and inflict damage on the enemy," he said.

In Kharkiv itself, Mayor Igor Terekhov was quoted by the city council as saying there was no reason for people to leave the city despite the offensive.

"Despite all the events that are taking place in the region, Kharkiv is calm. We do not see people leaving," he was quoted as saying.

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.

President Volodymyr Zelensky said on Saturday that Ukrainian troops had been carrying out counterattacks in the border villages.

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

Troops must "return the initiative to Ukraine," the president insisted, again urging Western 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.