• Russia focusing efforts on last Luhansk cities held by Ukraine
• Ukraine claims advances in southern Kherson region
• Separatist Donbas region sentences Britons, Moroccan to death
• Rising concern over food crisis as Russia blockades ports

KYIV/SLOVIANSK, Ukraine, June 9 (Reuters) - Ukrainian forces were holding their positions in intense street fighting in the eastern city of Sievierodonetsk, where Russians were "dying like flies", the region's governor said on Thursday, but they faced a "catastrophic" lack of artillery.

The battle amid the ruins of Sievierodonetsk, a small industrial city, has become one of the war's bloodiest, with Russia concentrating its invasion force there. Both sides say they have inflicted massive casualties.

In the self-proclaimed Donetsk People's Republic (DPR), one of Russia's proxies in eastern Ukraine, a court sentenced two Britons and a Moroccan who were captured while fighting for Ukraine to death, Russian news agencies reported.

In the south, Ukraine's defence ministry said it had captured new ground in a counter-attack in Kherson province, targeting the biggest swathe of territory Russia has seized since its invasion.

Thousands of people have been killed and millions have fled since Moscow launched its "special military operation" to disarm and "denazify" its neighbour on Feb. 24. Ukraine and its allies call the invasion an unprovoked war of aggression.

Speaking in Moscow to mark the 350th anniversary of Russian Tsar Peter the Great's birth, President Vladimir Putin drew a parallel between what he portrayed as their historic quests to win back what he called Russian lands.

TWIN CITIES

Sievierodonetsk and its twin city Lysychansk on the opposite bank of the Siverskyi Donets river are the last Ukrainian-controlled parts of Luhansk province, which Moscow is determined to seize as one of its principal war objectives.

"They (the Russians) are dying like flies ... fierce fighting continues inside Sievierodonetsk," said Luhansk governor Serhiy Gaidai in an online post.

Gaidai predicted the Russians would try to take advantage of low water levels to cross the Siverskyi Donets river. "We are watching and if anything happens we will act proactively."

Russian forces are focusing all of their might in the area, Ukraine's Security Council Secretary Oleksiy Danilov told Reuters in an interview on Thursday.

"They don't spare their people, they're just sending men like cannon fodder," he said. "They are shelling our military day and night."

Sievierodonetsk Mayor Oleksandr Stryuk said on Thursday around 10,000 civilians were still trapped inside the city - around a tenth of its pre-war population.

In a rare update from Sievierodonetsk, the commander of Ukraine's Svoboda National Guard Battalion, Petro Kusyk, said Ukrainians were drawing the Russians into street fighting to neutralise Russia's artillery advantage.

"Yesterday was successful for us - we launched a counteroffensive and in some areas we managed to push them back one or two blocks.