The evacuation of civilians from Sloviansk continued Wednesday as Russian troops pressed towards the eastern Ukrainian city in their campaign to control the Donbas region, as Ireland's prime minister visited Kyiv.

Sloviansk has been subjected to heavy bombardment in recent days as the invading Russian forces push westwards.

"Twenty years of work; everything is lost. No more income, no more wealth," Yevgen Oleksandrovych, 66, told AFP as he surveyed the site of his auto parts shop, destroyed in Tuesday's strikes.

AFP journalists saw rockets slam into Sloviansk's marketplace and surrounding streets, with firefighters scrambling to put out the resulting blazes.

Around a third of the market in Sloviansk appeared to have been destroyed, with locals coming to see what was left among the charred wreckage.

The remaining part of the market was functioning, with a trickle of shoppers coming out to buy fruit and vegetables.

"I will sell it out and that's it, and we will stay home. We have basements, we will hide there. What we can do? We have nowhere to go, nobody needs us," said 72-year-old greengrocer Galyna Vasyliivna.

Mayor Vadym Lyakh said that around 23,000 people were still in Sloviansk but claimed Russia had been unable to surround the city.

"Since the beginning of hostilities, 17 residents of the community have died, 67 have been injured," he said.

"Evacuation is ongoing. We take people out every day. About 23,000 residents remain. Many of the evacuees were taken by bus to the city of Dnipro, further west.

"The city is well fortified. Russia does not manage to advance to the city," he said.

Vitaliy, a plumber, said his wife and their daughter, who is six months pregnant, were evacuated from Sloviansk on Wednesday.

"I am afraid for my wife," he told AFP.

"Here, after what happened yesterday, they hit the city centre; need to leave.

"I sent my wife, and I have no more choice: tomorrow I will join the army."

Russians push west 

The eastern Donbas is mainly comprised of Lugansk region, which Russian forces have almost entirely captured, and the Donetsk region to its southwest -- the current focus of Moscow's attack and the location of Sloviansk.

The fall of Lysychansk in Lugansk on Sunday, a week after the Ukrainian army also retreated from the neighbouring city of Severodonetsk, has freed up Russian troops to advance west on Kramatorsk and Sloviansk in Donetsk.

On Tuesday, they were first closing in on the smaller city of Siversk -- which lies between Lysychansk and Sloviansk -- after days of shelling there.

Donetsk governor Pavlo Kyrylenko said Russian forces killed five civilians and injured 21 in the region on Tuesday.

Lugansk governor Sergiy Gayday claimed that Ukrainian forces were holding back Russian troops on the borders of Lugansk and Donetsk.

"Yesterday Russians wanted to advance towards Donetsk Oblast and to cut the Bakhmut-Lysychansk highway going through Bilogorivka, but have nothing to report to their chiefs. The enemy had to retreat because of our army's pressure," he said.

He insisted that Russia did not control the entire Lugansk region, saying they had not reached the administrative border.

"Fighting still keeps going in two villages," he said.

Irish PM visits Kyiv 

Ukrainian President Volodymyr Zelensky, speaking in his evening address Tuesday, said he was continuing to press Western allies for upgraded anti-missile systems as air siren alerts sounded across much of the country, including the capital.

Irish Prime Minister Micheal Martin was in Kyiv on Wednesday to voice Dublin's solidarity and discuss how Ireland can support the country's needs.

"The people of Ireland stand with Ukraine and its people in the face of Russia's immoral and unprovoked war of terror," he said.

"The bombardment and attacks on civilians are nothing short of war crimes."

Martin said Ireland supported Ukraine's push for membership of the European Union.

The EU on Wednesday set out a harder focus on energy given Russia's war in Ukraine.

"We need to prepare for further disruptions of gas supply, even a complete cut-off from Russia," European Commission chief Ursula von der Leyen told the European Parliament.

The EU has launched a 300-billion-euro ($310-billion) plan to wean itself off Russian fossil fuel supplies, and is also investing heavily to transform the market towards renewable sources.

Meanwhile former Russian president Dmitry Medvedev invoked the possibility of nuclear war if the International Criminal Court moves to punish Moscow for alleged crimes in Ukraine since the February 24 invasion.

"The idea to punish a country that has the largest nuclear arsenal is absurd," Medvedev, a close ally of President Vladimir Putin, said on messaging app Telegram.

"And potentially creates a threat to the existence of mankind."