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WRAPUP 5-Heavy fighting as Russian troops enter outskirts of Ukraine's Sievierodonetsk

* Russian forces enter fringes of Sievierodonetsk - governor

* Ukraine pleads for more weapons from West

* Borrell says EU will agree on next sanctions package

By Pavel Polityuk and Natalia Zinets

KYIV, May 30 (Reuters) - Russian troops have entered the outskirts of the Ukrainian city of Sievierodonetsk, according to the regional governor, who described fierce fighting on Monday over the ruins of a city that has become the focus of Moscow's offensive.

The European Union has sought to make Moscow pay a heavy price for invading Ukraine, but leaders arriving for a summit acknowledged they were unlikely to pass a new round of sanctions yet, having failed to agree to ban imports of Russian oil.

Russia has concentrated its firepower on the last major population centre still held by Ukrainian forces in the eastern Luhansk province, in a push to achieve one of President Vladimir Putin's stated objectives after three months of war.

Incessant shelling has left Ukrainian forces defending ruins in Sievierodonetsk, but their refusal to withdraw has slowed the wider Russian offensive across the Donbas region. Luhansk region governor Serhiy Gaidai said Russian troops had advanced into the city's southeastern and northeastern fringes.

The Russians "use the same tactics over and over again. They shell for several hours - for three, four, five hours - in a row and then attack", Gaidai said.

"Those who attack die. Then shelling and attack follow again, and so on until they break through somewhere."

With temperatures rising, he said there was a "terrible smell of death" on the outskirts of the city.

But he said Ukrainian forces had driven the Russians out of the village of Toshkivka to the south, potentially frustrating Moscow's push to encircle the area.

Gaidai later said a French journalist had been killed by shrapnel that pierced his vehicle, and that evacuations from the area had been halted.

In a televised speech, Ukrainian President Volodymyr Zelenskiy described capturing Sievierodonetsk as "a fundamental task for the occupiers".

"Some 90% of buildings are damaged. More than two-thirds of the city's housing stock has been completely destroyed," he said.

Ukraine's defence ministry said Moscow was also trying to regroup to attack the strategically important town of Sloviansk, further west.

EU DEADLOCK

The EU's latest sanctions package has been blocked by landlocked Hungary's refusal to agree to a ban on imports of Russian oil, which it receives through the huge Soviet-era "Friendship" pipeline.