KYIV, May 31 (Reuters) - Ukraine said on Tuesday that Russia had taken control of most of the eastern industrial city of Sievierodonetsk, a bombed-out wasteland whose capture Moscow has made the principal objective of its invasion.

Russia's all-out assault on the city in Ukraine's Luhansk province has been met by tough resistance from Ukrainian forces. Russian-backed separatists in Luhansk acknowledged that capturing the city was taking longer than hoped, despite one of the biggest ground attacks of the three-month-long war.

After failing to capture the Ukrainian capital Kyiv and being driven out of northern Ukraine, a Russian victory in Sievierodonetsk and across the Siverskyi Donets river in Lysychansk would bring full control of Luhansk, one of two eastern provinces Moscow claims on behalf of separatists.

Western military analysts say Moscow has drained manpower and firepower from other parts of the eastern front to concentrate on Sievierodonetsk, hoping a massive offensive will secure surrounding Luhansk province for separatist proxies.

Luhansk's regional governor, Serhiy Gaidai, said nearly all critical infrastructure in Sievierodonetsk had been destroyed and 60% of residential property damaged beyond repair.

"Most of Sievierodonetsk is under the control of the Russians. The town is not surrounded and the prerequisites for it to be are not in place," Gaidai said. Russian shelling had made it impossible to deliver aid or evacuate people, he added.

A pro-Moscow separatist leader said that fighting was raging in the city but that Russian proxies had advanced slower than expected to "maintain the city's infrastructure" and exercise caution around its chemical factories.

"We can say already that a third of Sievierodonetsk is already under our control," Russia's TASS state news agency quoted Leonid Pasechnik, the leader of the pro-Moscow Luhansk People's Republic, as saying.

Gaidai warned Sievierodonetsk residents not to leave bomb shelters due to what he said was a Russian air strike on a nitric acid tank. The Luhansk People's Republic's police force said Ukraine's forces had damaged it. Ukraine and Russian-backed separatists traded accusations over a similar incident in April.