Ukrainian President Volodymyr Zelenskiy called the current situation in the Donbas region "very difficult" as Russian forces and Moscow-backed separatists attacked the last Ukrainian strongholds in the eastern Luhansk region.
Russian forces have concentrated their efforts in the Donbas, Zelenskiy said, using maximum artillery fire and missile strikes as Ukrainian forces "protect our land in the way that our current defense resources allow."
The fighting on May 27 focused on the cities of Syevyerodonetsk and Lysychansk -- the last areas under Ukrainian control in Luhansk.
Serhiy Hayday, the governor of Luhansk region, said that Ukrainian forces are engaged in a "fierce defense" of Syevyerodonetsk, which is two-thirds surrounded by Russian forces.
"The Russians will not be able to capture Luhansk region in the coming days as analysts have predicted," Hayday said on Telegram, referring to Syevyerodonetsk and Lysychansk, which lies across the Siverskiy Donets River.
"We will have enough strength and resources to defend ourselves. However, it is possible that in order not to be surrounded we will have to retreat," he said.
He said earlier that "very strong" shelling has destroyed 90 percent of the housing in the city.
The Defense Ministry says the current phase of the war is the most active full-scale military aggression thus far.
The Ukrainian military reported that eight attacks by Russian troops had been repulsed in Donetsk and Luhansk during the day, while fighting continued at five locations.
Zelenskiy said Russian forces are trying to achieve some success by next week when the 100th day of the war will be marked.
"The occupiers are trying to achieve in 100 days of war those goals that they hoped to achieve in the first days after February 24," Zelenskiy said in his nightly address.
Syevyerodonetsk Mayor Oleksandr Stryuk said that at least 1,500 people have been killed in his city since the start of Russia's invasion in late February. About 12,000 to 13,000 remain in the city -- down from a prewar population of about 100,000, he said.
Moscow-backed separatists on May 27 also claimed full control of the important battlefield town of Lyman, some 60 kilometers west of Syevyerodonetsk, but the Ukrainian Defense Ministry denied that the major railway hub had fallen, saying in a statement that its forces continue to counteract Russian attempts to overrun it.
Lyman has been a front line target as Russian forces press down from the north, one of three directions from which they have been attacking Ukraine's industrial Donbas region.
On the diplomatic front, Austrian Chancellor Karl Nehammer says he and Russian President Vladimir Putin discussed a possible prisoner swap and blocked shipments of Ukrainian grain during a phone call on May 27.
Nehammer, who spoke to reporters after the 45-minute call, said Putin told him that Moscow is ready to discuss a prisoner swap with Ukraine but the question is complex. The Austrian leader said his impression during the call was that Putin wants to create facts on the ground that he can take into negotiations.
Zelenskiy said earlier that he must hold talks with Putin in order to safeguard Ukraine's sovereignty and existence.
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Zelenskiy said in an address on May 27 to an Indonesian think tank that Ukraine was not longing to talk to Putin, but that it has to face the reality that this will likely be necessary to end the war that Moscow launched against it on February 24.
"There are things to discuss with the Russian leader. I'm not telling you that our people are eager to talk to him, but we have to face the reality of what we are living through," Zelenskiy said.
"What do we want from this meeting?...We want our lives back...We want to reclaim the life of a sovereign country within its own territory," he said, adding that Russia did not appear to be ready yet for serious peace talks.
Zelenskiy also accused Russia -- which has said it would allow Ukraine to resume its grain exports by sea if the West lifts some sanctions imposed on it for starting the war -- of weaponizing the global food supply crisis.
The last known face-to-face talks between Russian and Ukrainian negotiators were held on March 29. Negotiations continued online for a while but both sides now say they have stopped.
According to a Kremlin statement, Putin informed Nehammer about actions that Russia is taking to secure safe passage for vessels in the Sea of Azov and the Black Sea.
Putin told Nehammer that attempts to blame Russia for difficulties shipping grain worldwide were unfounded and pointed to Western sanctions being responsible instead, according to the Kremlin.
"Detailed explanations have been given of the real causes of these problems, which have emerged due to anti-Russian sanctions by the United States and the European Union, among other things,” the statement said.