Ukrainians were digging in to defend the city of Sievierodonetsk, in the eastern Luhansk province, as its governor accused Russian forces of attempting to "destroy" the area with heavy bombardment on Sunday.
"Today, from 50 up to 100 people may die in the most difficult direction, in the east of our state," President Zelenskyy said during a press conference with Polish President Andrzej Duda.
"They are defending our state and our independence, which everyone in the world is talking about... We personally feel it very much."
Mr Zelenskyy's warnings came as the UN Refugee Agency (UNHCR) said the number of displaced people globally has crossed the "staggering milestone" of 100 million for the first time, propelled by the war in Ukraine and other conflicts.
Eight million have been displaced within Ukraine and more than six million refugees from the war-torn country have been registered.
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“One hundred million is a stark figure – sobering and alarming in equal measure. It’s a record that should never have been set,” said UN High Commissioner for Refugees, Filippo Grandi.
He said the international response to Ukrainians fleeing the war has been "overwhelmingly positive" and urged for similar mobilisation for "all crises around the world".
"But ultimately, humanitarian aid is a palliative, not a cure," he added.
"To reverse this trend, the only answer is peace and stability so that innocent people are not forced to gamble between acute danger at home or precarious flight and exile.”
Ukrainian and Russian forces battled along a 342-mile wedge of the country's eastern industrial heartland, the Donbas, on Sunday, as the Kremlin attempted to expand the territory Moscow-backed separatists have held since 2014.
Sievierodonetsk is now the main city under Ukrainian control in the Luhansk province of the Donbas, whose governor Serhii Haidai accused the Russians of “trying to destroy the city" by "engaging in a scorched-earth approach.”
Mr Haidai said the Russians had occupied several towns and cities in Luhansk after indiscriminate, 24-hour shelling and were concentrating forces and weaponry there, bringing in troops from Kharkiv to the northwest, Mariupol to the south, and from inside Russia.
The only working hospital in Sievierodonetck has only three doctors and supplies for 10 days, he warned.
To bolster its defences, Ukraine’s parliament on Sunday voted to extend martial law and the mobilisation of armed forces for a third time, until August 23.
Concerns also grew for more than 2,400 Ukrainian fighters who are now in Russian hands after the invading forces claimed the besieged Mariupol steel works is now fully under their control.
While forces battled on the frontline, Polish President Andrzej Duda traveled to Kyiv on Sunday to support Ukraine’s European Union aspirations and addressed Ukraine's parliament.
Mr Zelenskyy has urged the 27-member EU to expedite his country’s request to join. It is to be discussed at a Brussels summit in late June.
He called Mr Duda's visit - his second since April - “a historic opportunity not to lose such strong relations, built through blood, through Russian aggression. All this not to lose our state, not to lose our people.”
The conflict is not confined to Ukraine’s east. Powerful explosions were heard early Monday in Korosten, about 100 miles west of Kyiv, the town’s deputy mayor said. It was the third straight day of apparent attacks in the Zhytomyr District, Ukrainian news agencies reported.
In the Russian-held city of Enerhodar, 174 miles north-west of Mariupol, an explosion on Sunday injured the Moscow-appointed mayor at his residence, Ukrainian and Russian news agencies reported.
Ukraine’s Unian news agency said a bomb planted by “local partisans” wounded 48-year-old Andrei Shevchuk, who lives near the Zaporizhzhia nuclear power plant, Europe’s largest.