President Volodymyr Zelensky said Ukrainian troops were engaged in fierce street fighting with Russian soldiers in the industrial city of Sievierodonetsk, a pivotal battle in the Kremlin's attempt to control the eastern Donbas region.

"Our heroes do not give up positions in Sievierodonetsk. In the city, fierce street fighting continues," Zelensky said in his nightly video address on Monday.

"And the Ukrainian Donbas stands, stands strong," he added referring to the region where Sievierodonetsk is located.

It was unclear which side had the upper hand, with "the situation changing from hour to hour", Oleksandr Stryuk, head of administration in Sievierodonetsk, said on television.

The city has become the main target of the Russian offensive in the Donbas - comprising Luhansk and Donetsk provinces - as the Kremlin's invasion grinds on in a war of attrition that has seen cities laid waste by artillery barrages.

Ukraine's defence ministry said Russia was also throwing troops and equipment into its drive to capture the largest remaining Ukrainian-held city in Luhansk.

Luhansk Governor Serhiy Gaidai said earlier on Monday the situation had worsened after Ukrainian defenders had pushed back the Russians over the weekend as they seemed close to victory.

In its nightly update, the Ukrainian military said two civilians were killed in Russian shelling in the Donetsk and Luhansk regions on Monday and that Russian forces had fired at more than 20 communities.

Reuters could not independently verify the battlefield reports. Russia denies targeting civilians in the conflict.

Russia says it is on a mission to "liberate" the Donbas - partly held by separatist proxies of Moscow since 2014 - after Ukrainian forces pushed its troops back from the capital Kyiv and Ukraine's second city Kharkiv in the war's early stages.

Russia invaded Ukraine on February 24, but calls its action a "special military operation" to stamp out what it sees as threats to its security. Ukraine and its Western allies call this a baseless pretext for a war to grab territory that risks turning into a wider European conflict.

Constant shelling

Ukraine's defence ministry said on Monday that Russian forces were also advancing towards Sloviansk, which lies about 85km to the west of Sievierodonetsk.

"The front line is under constant shelling," Donetsk regional governor Pavlo Kyrylenko told Ukrainian television.

"The enemy is also shelling near Lyman with the aim of wrecking our defensive positions and advancing on Sloviansk and Kramatorsk. There is also shelling of Svyatohirsk with the same aim."

Kyrylenko said efforts were underway to evacuate people from several towns, some under day and night attack, including Sloviansk which has about 24,000 residents still there.

"People are now understanding, though it is late, that it is time to leave," he said.

In a move coordinated with the United States, Britain said it would supply Ukraine with multiple-launch rocket systems that can strike targets up to 80km away, providing the more precise, long-range firepower needed to reach Russian artillery batteries, a key component of Moscow's battle plans.

Zelensky said Kyiv was gradually receiving "specific anti-ship systems", and that these would be the best way to end a Russian blockade of Ukrainian Black Sea ports preventing grain exports.

Russian Foreign Minister Sergei Lavrov said Moscow would respond to Western deliveries of long-range weapons by pushing Ukrainian forces further back from Russia's border.

On Sunday, President Vladimir Putin said Russia would strike new targets if the West supplied longer-range missiles. The same day, Russian missiles hit Kyiv for the first time in more than a month.

The US, which reopened its embassy in Kyiv in May after an almost three-month closure, said its embassy posture in the Ukrainian capital remains unchanged.

Western countries have imposed sanctions of unprecedented sweep and severity on Russia over its invasion.

On Monday, Russia's foreign ministry said it had slapped personal sanctions on 61 U.S. officials including the treasury and energy secretaries and leading defence and media executives. The move, it said, was in retaliation for "constantly expanding U.S. sanctions". Fierce street fighting in Ukraine's SievierodonetsK.