* Russian forces pour resources into battle
* City of Sievierodonetsk under assault
* Ukraine pleads for more weapons from West
* EU cannot agree on Russian oil embargo; more talks Monday
By Max Hunder and Mari Saito
KYIV/KHARKIV, Ukraine, May 29 (Reuters) - Russian forces intensified their attacks with barrages of heavy artillery to capture a key Ukrainian city in the southeastern region of Donbas, whose full takeover Moscow's top diplomat said was now an "unconditional priority".
Constant Russian shelling has destroyed all of the critical infrastructure in Sievierodonetsk, the largest city Ukraine still controls in Luhansk, one of the regions in Donbas, Ukrainian President Volodymyr Zelenskiy said, while pledging to do everything to hold off the advance.
"Some 90% of buildings are damaged. More than two-thirds of the city's housing stock has been completely destroyed. There is no telecommunication," he said in a televised speech.
"Capturing Sievierodonetsk is a fundamental task for the occupiers ... We do all we can to hold this advance," he added.
The "liberation" of the Donbas, an industrial region which includes Luhansk and Donetsk, is an "unconditional priority" for Russia, Foreign Minister Sergei Lavrov said on Sunday.
In a Facebook post, Ukrainian forces in the Donbas said they had been on the defensive all day on Sunday. Russian forces fired on 46 communities in the Donetsk and Luhansk regions, killing at least three civilians, wounding two others or destroying or damaging 62 civilian buildings.
Russian shelling also continued across several regions such as in Novy Buh in Mykolaiv and Sumy. The city council in Novy Buh in Mykolaiv region in southern Ukraine said on its Telegram channel that a Russian missile attack had caused considerable damage in the city centre.
The battle for Sievierodonetsk, which lies on the eastern bank of the Siverskyi Donets River, is in the spotlight as Russia ekes out slow but solid gains in the part of the country close to the Russian border.
Having failed to take the capital Kyiv in the early phase of the war, Russia is seeking to consolidate its grip on the Donbas, large parts of which are already controlled by Moscow-backed separatists.
It has concentrated huge firepower on a small area - a contrast to earlier phases of the conflict when its forces were often spread thinly - bludgeoning towns and cities with artillery and air strikes.
The Ukrainian government meanwhile urged the West to provide it with more longer-range weapons in order to turn the tide in the war, now in its fourth month. Zelenskiy voiced hopes that the weapons would be provided and that he expected "good news" in the coming days.
U.S. officials have said such weapons systems are actively being considered.
Analysts at the Institute for the Study of War in Washington said the Russians had still not managed to encircle Sievierodonetsk and the Ukrainian defenders have inflicted "fearful casualties" on them.
The Ukrainians were taking serious losses themselves, civilians as well as combatants, they said in a briefing paper.
Russia's focus on Sievierodonetsk had drawn resources from other battlefronts and as result they had made little progress elsewhere, the analysts said.
A Reuters journalist in the area said a ceramics factory was almost completely destroyed on the outskirts of the Donetsk town of Bakhmut, which straddles the last main road into Sievierodonetsk and is just 10 km (6 miles) from the frontline.
The journalist heard what appeared to be outgoing artillery fire and Russian aircraft dropping a bomb close to the town. Several transporters with Ukrainian soldiers could be seen in the area.
EMBARGO ON RUSSIAN OIL
Russia says its "special military operation" aims to rid Ukraine of nationalists threatening Russian-speakers. Ukraine and Western countries say Russia's claims are a false pretext for a war of aggression and the West has imposed a barrage of sanctions targeting Moscow while delivering shipments of weapons to help the Ukrainian government defend itself.
However, after nearly half a dozen rounds of punitive measures, some against oligarchs close to Russian President Vladimir Putin and banks, the unity within the European Union is being put to fresh test as the bloc on Sunday failed to agree on an embargo of Russian oil. Talks will continue on Monday.
German Economy Minister Robert Habeck expressed fears that EU unity was "starting to crumble". The bloc's leaders are set to meet on Monday and Tuesday in a summit to discuss a new sanctions package against Russia including the oil embargo.
Meanwhile Zelenskiy - who has won widespread admiration in the West for his leadership in the conflict - visited Ukrainian troops on the frontlines in northeastern Kharkiv region.
Several explosions were heard in Kharkiv city hours after Sunday's visit, a Reuters journalist said, in what was Zelenskiy's first trip outside the Kyiv region since the invasion began.
A large plume of smoke could be seen rising northeast of the centre of the city, which has been the target of Russian shelling in recent days after several weeks of relative quiet.
"You risk your lives for us all and for our country," the president's office quoted him as telling soldiers as he handed out commendations and gifts.
(Reporting by Natalia Zinets, Conor Humphries, Pavel Polityuk and Bogdan Kochubey in Kyiv, David Ljunggren in Ottawa, Lidia Kelley in Melbourne; Writing by Angus MacSwan and Humeyra Pamuk; Editing by Grant McCool and Stephen Coates)