Russian and Ukrainian troops engaged in close-quarter combat in an eastern Ukraine city on Sunday as Moscow’s soldiers, supported by intense shelling, attempted to gain strategic footholds for conquering the region in the face of fierce Ukrainian resistance.

Ukrainian regional officials reported Russian forces “storming” Sievierodonetsk after trying unsuccessfully to encircle the city.

The fighting knocked out power and mobile phone service, and a humanitarian relief centre could not operate because of the danger, the mayor said.

Sievierodonetsk, located about 89 miles south of the Russian border, emerged in recent days as the epicentre of Moscow’s quest to capture all of Ukraine’s industrial Donbas region.

Russia also stepped up its efforts to take nearby Lysychansk, where civilians rushed to escape persistent shelling.

The two eastern cities span the strategically-important Siverskiy Donetsk river. They are the last major areas under Ukrainian control in Luhansk province, which makes up the Donbas together with neighbouring Donetsk.

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Ukrainian President Volodymyr Zelensky as he visits the Kharkiv region (Ukrainian Presidential Press Office via AP)

Ukrainian President Volodymyr Zelensky made a rare frontline visit to the city of Kharkiv as he sought to assert the strength of Ukraine’s position there.

Ukrainian fighters pushed Russian forces back from positions near the city, Ukraine’s second-largest, several weeks ago.

“I feel boundless pride in our defenders. Every day, risking their lives, they fight for Ukraine’s freedom,” Mr Zelensky wrote on the Telegram messaging app after visiting soldiers stationed in Kharkiv.

Russia has kept up its bombardment of the north-eastern city from afar, and explosions could be heard in the area shortly after Mr Zelensky’s visit.

Shelling and air strikes have destroyed more than 2,000 apartment buildings since Russia invaded Ukraine on February 24, according to the regional governor, Oleh Syniehubov.

In the wider Kharkiv region, Russian troops still held about 30% of the territory, while Kyiv’s troops had recaptured another 5%, the governor said.

However, Mr Zelensky acknowledged that the battle for the east is “indescribably difficult”.

The “Russian army is trying to squeeze at least some result” by concentrating its attacks there, he said in a Saturday night video address.

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Debris hangs from a residential building heavily damaged in a Russian bombing in Bakhmut, eastern Ukraine (Francisco Seco/AP)

Russia is focused, after failing to seize Ukraine’s capital, on occupying parts of Donbas not already controlled by pro-Moscow separatists.

Russian forces made small advances in recent days as bombardments chewed away at Ukrainian positions and kept civilians trapped in basements or desperately trying to get out safely.

Attacks to destroy military targets throughout the country also caused casualties in civilian areas.

Civilians who reached the eastern city of Pokrovsk, about 80 miles south of Lysychansk, said they held out as long as they could before fleeing the Russian advance.

Yana Skakova choked back tears as she described leaving with her 18-month and four-year-old sons while her husband stayed behind to take care of their house and animals.

The family was among 18 people who lived in a basement for the past two-and-a-half months until police told them on Friday it was time to evacuate.

“None of us wanted to leave our native city,” she said. “But for the sake of these small children, we decided to leave.”

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Volodymyr Zelensky described the situation in the east as ‘indescribably difficult’ (Ukrainian Presidential Press Office via AP)

Serhiy Haidai, the provincial governor of Luhansk, said constant shelling created a “severe” situation in Lysychansk.

“There are fatalities and wounded people,” he wrote on Telegram, without elaborating.

On Saturday, he said, one civilian died and four were injured after a Russian shell hit a high-rise apartment building.

But some Luhansk supply and evacuation routes still functioned on Sunday, he said.

He claimed the Russians had retreated “with losses” from around a village near Sievierodonetsk but conducted air strikes on another nearby village located on the strategic Siverskiy Donetsk river.

Sievierodonetsk Mayor Oleksandr Striuk said there was fighting at the city’s bus station on Saturday.

Residents remaining in the city, which had a pre-war population of around 100,000, risked exposure to shelling to get water from a half-dozen wells, and there was no electricity or mobile phone service, Mr Striuk said.

Mr Striuk has estimated that 1,500 civilians have died in Russian attacks since the beginning of the war, as well as from a lack of medicine and diseases that could not be treated.