Ukrainian President Volodymyr Zelenskiy on Sunday (local time) accused Russian soldiers of committing war crimes and killing civilians in Kherson, parts of which were retaken by Ukraine's army last week after Russia pulled out.

"Investigators have already documented more than 400 Russian war crimes. Bodies of dead civilians and servicemen have been found," Zelenskiy said in his nightly video address.

"The Russian army left behind the same savagery it did in other regions of the country it entered," he said.

Reuters was unable immediately to verify his allegations. Russia denies its troops intentionally target civilians.

Utility companies in southern Kherson region were working to restore critical infrastructure damaged and mined by fleeing Russian forces, with most homes in the southern Ukrainian city still without electricity and water, regional officials said.

Ukrainian troops arrived in the centre of Kherson on Friday after Russia abandoned the only regional capital it had captured since Moscow launched its invasion in February.

The withdrawal marked the third major Russian retreat of the war and the first to involve yielding such a large occupied city in the face of a major Ukrainian counter-offensive that has retaken parts of the east and south.

On Sunday, artillery exchanges echoing over the city failed to discourage crowds of jubilant, flag-waving residents bundled up against the cold from gathering on Kherson's main square. The crowds tried to catch mobile phone signals from Starlink ground stations carried on Ukrainian military vehicles.

"First their special police went. Then the ordinary police and their administration. Then you started seeing fewer soldiers in the supermarkets and then their military vehicles driving away."

"We are happy now, but all of us are afraid of the bombing from the left bank," said Yana Smyrnova, 35, a singer, referring to Russian guns on the east side of the Dnipro River that runs close to the city.

Smyrnova said she and her friends had to get water from the river for bathing and flushing their toilets, and only a few residents were lucky enough to have generators that power pumps to get water from wells.

The governor of Kherson region, Yaroslav Yanushevych, said the authorities had decided to maintain a curfew from 5pm to 8am and ban people from leaving or entering the city as a security measure.

"The enemy mined all critical infrastructure," Yanushevych told Ukrainian TV. "We are trying to meet within a few days and (then) open the city," he said.

Local authorities said most of the city lacked electricity or water. Yuriy Sobolevskiy, first deputy chairman of Kherson regional council, told Ukrainian TV that even as the authorities were working to restore critical services, the humanitarian situation remained "very difficult".

'OUR BOYS AND GIRLS'

Some of those celebrating at Kherson's main square, however, said the difficulties paled compared with the joy of seeing Ukrainian troops entering the city.

"When we saw our army, all of the problems with water and electricity disappeared," said Yana Shaposhnikova, 36, a clothing designer. "The explosions are not so scary. Our boys and girls (troops) are here. So it's not so scary."

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Officials reported some early progress in restoring normality to the city.

Zelenskiy's adviser Kyrylo Tymoshenko said on Telegram that a mobile connection was already working in the city centre, while the head of Ukrainian state railways said train services to Kherson were expected to resume this week.

Residents said the Russians had pulled out gradually over the past two weeks, but their final departure became clear only when the first Ukrainian troops entered Kherson on Thursday.

"The level of Russian attacks has not declined. And the level of our resilience and courage is at its highest. We will not allow them through our defence."

"It was a gradual thing," said Alexii Sandakov, 44, a videographer. "First their special police went. Then the ordinary police and their administration. Then you started seeing fewer soldiers in the supermarkets and then their military vehicles driving away."

Many residents interviewed by Reuters said they tried to minimize their contact with the Russians and knew of people who were arrested and abused for showing any expression of Ukrainian patriotism.

Reuters could not immediately verify such accounts.

Russia has denied abuses against civilians or attacks on civilians since the war began.

"We had to bury our (Ukrainian) flag," said Shaposhnikova, who sported a New York Yankees baseball cap. "If you wore anything yellow and blue (the Ukrainian national colours) you could be shot or invited into a cellar where you would be tortured."

She said Russian police had arrested a friend of hers who was a volunteer delivering humanitarian aid to outlying areas. They took her to an underground jail and deprived her of sleep for three days while interrogating her, demanding to know whether she was revealing their positions to the Ukrainian military, Shaposhnikova said.

Sandakov said Russian troops had looted the homes of Ukrainian soldiers who left the city before the takeover and would inspect the bodies of young men passing through checkpoints for tattoos of Ukrainian nationalist groups.

Reuters could not independently verify these comments.

EASTERN UKRAINE

Ukraine's defence ministry said it had recaptured 179 settlements and 4,500 square kilometres (1,700 square miles) along the Dnipro River since the beginning of the week.

Ukrainian armed forces' general staff reported continued fierce fighting along the eastern front in the Donetsk and Luhansk regions. Over the past 24 hours, there have been missile and artillery strikes in Sumy, Kharkiv, Zaporizhzhia, Luhansk and Donetsk, Zelenskiy said.

"The level of Russian attacks has not declined. And the level of our resilience and courage is at its highest. We will not allow them through our defence."