KYIV, July 1 (Reuters) - Ukraine on Friday celebrated driving Russian forces from the strategic Black Sea outpost of Snake Island while struggling to hold off intense assaults in the eastern industrial city of Lysychansk.

Russia said on Thursday it had decided to withdraw from Snake Island as a "gesture of goodwill" to show Moscow was not obstructing U.N. attempts to open a humanitarian corridor allowing grains to be shipped from Ukraine.

Ukraine said it had driven Russian forces off the outcrop after an artillery and missile assault, with President Volodymyr Zelenskiy hailing the strategic win.

"It does not yet guarantee security. It does not yet ensure that the enemy will not come back," he said in his nightly video address. "But this significantly limits the actions of the occupiers. Step by step, we will push them back from our sea, our land and our sky."

In contrast, however, Ukrainian forces were desperately hanging on against Russia's superior firepower in the city of Lysychansk.

Russian artillery shelled from different directions while the Russian army approached from several sides, regional Governor Serhiy Gaidai said on Ukrainian television.

"The superiority in fire power of the occupiers is still very much in evidence," Zelenskiy said. "They have simply brought in all their reserves to hit us."

Russian forces have been trying to encircle Lysychansk since they captured Sievierodonetsk, on the opposite side of the Siverskyi Donets River, last week after weeks of heavy fighting.

In Sievierodonetsk, residents have emerged from their basements and are sifting through the rubble of their ruined city as they look to rebuild.

"Almost all the city infrastructure is destroyed. We are living without gas, electricity, and water since May," Sergei Oleinik, a 65-year-old resident told Reuters. "We are glad that this ended, and soon maybe reconstruction will start, and we will be back to more or less normal life."