After ending weeks of resistance by the last Ukrainian fighters in the strategic southeastern city of Mariupol, Russia is waging what appears to be a major offensive in Luhansk, one of two provinces in Donbas.
Russian-backed separatists already controlled swathes of territory in Luhansk and the neighbouring Donetsk province before the February 24 invasion.
Moscow now wants to seize the last remaining Ukrainian-held territory in Donbas.
"The situation in Donbas is extremely difficult," Ukrainian President Volodymyr Zelenskiy said in his nightly address on Saturday.
The Russian army was trying to attack the cities of Sloviansk and Sievierodonetsk, but Ukrainian forces were holding off their advance, he said.
Earlier, Zelenskiy told local television that while the fighting would be bloody, the end would come only through diplomacy and that the Russian occupation of Ukrainian territory would be temporary.
Zelenskiy adviser Mykhailo Podolyak ruled out agreeing to a ceasefire and said Kyiv would not accept any deal with Moscow that involved ceding territory.
He said making concessions would backfire on Ukraine because Russia would hit back harder after any break in fighting.
"The war will not stop (after concessions). It will just be put on pause for some time," Podolyak, Ukraine's lead negotiator, told Reuters in an interview in the heavily guarded presidential office.
"They'll start a new offensive, even more bloody and large-scale."
Recent calls for an immediate ceasefire have come from US Defence Secretary Lloyd Austin and Italian Prime Minister Mario Draghi.
The end of fighting in Mariupol, the biggest city Russia has captured, could be crucial to its ambitions in Donbas.
It gives Russian President Vladimir Putin a rare victory after a series of setbacks in nearly three months of combat.
The last Ukrainian forces holed up Mariupol's vast Azovstal steelworks surrendered on Friday, Russia said.
Full control of Mariupol gives Russia command of a land route linking the Crimean Peninsula, which Moscow seized in 2014, with mainland Russia and areas of eastern Ukraine held by pro-Russia separatists.
Ukrainian forces in the separatist-controlled regions of Luhansk and Donetsk said on Saturday they had repelled nine attacks and destroyed five tanks and 10 other armoured vehicles in the previous 24 hours.
Russian forces were using aircraft, artillery, tanks, rockets, mortars and missiles along the entire front line to attack civilian structures and residential areas, the Ukrainians said in a Facebook post.
At least seven people were killed in the Donetsk region, they said.
Russia's state gas company Gazprom said it halted gas exports to Finland, which refused Moscow's demands to pay in roubles for Russian gas after Western countries imposed sanctions over the invasion.
Finland and Sweden applied this week to join the NATO military alliance.
Finnish state-owned gas wholesaler Gasum, the Finnish government and individual gas consuming companies in Finland have said they were prepared for a shutdown of Russian flows.
Most European supply contracts are denominated in euros or US dollars. Last month, Moscow cut off gas to Bulgaria and Poland after they refused to comply with the new terms.
Western nations also have stepped up weapons supplies to Ukraine.
On Saturday, Kyiv got another huge boost when US President Joe Biden signed a bill to provide nearly $US40 billion ($A57 billion) in military, economic and humanitarian aid.
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