Ukraine has ruled out a ceasefire or any territorial concessions to Russia, and Poland's president has warned against appeasing Russian President Vladimir Putin.
Air raid sirens blared across Ukraine on Monday morning, sounding the daily alarm ahead of anticipated attacks by Russian forces in the east and south of the country.
Russia stepped up its pounding of the Donbas and Mykolaiv regions with air strikes and artillery fire, in what Ukraine has described as a "scorched-earth" strategy to win control of the eastern front.
"The war must end with the complete restoration of Ukraine's territorial integrity and sovereignty," Andriy Yermak, Ukraine's presidential chief of staff said in a Twitter post.
Polish President Andrzej Duda offered Warsaw's backing, telling lawmakers in Kyiv on Sunday that the international community had to demand Russia's complete withdrawal and that sacrificing any territory would be a "huge blow" to the entire West.
"Worrying voices have appeared, saying that Ukraine should give in to Putin's demands," Duda said, the first foreign leader to address the Ukrainian parliament in person since Russia's February 24 invasion.
"Only Ukraine has the right to decide about its future."
Ukraine's lead negotiator, Zelenskiy adviser Mykhailo Podolyak, ruled out any territorial concessions and rejected calls for an immediate ceasefire, saying any concessions would backfire because Russia would use the break in fighting to come back stronger.
Recent calls for an immediate ceasefire have come from US Defence Secretary Lloyd Austin and Italian Prime Minister Mario Draghi.
Ukraine and Poland agreed to establish a joint border customs control and work on a shared railway company to ease the movement of people and increase Ukraine's exports.
Most Ukrainian refugees have crossed to the European Union through border points in Poland, Slovakia, Hungary and Romania.
Poland has granted the right to live and work and claim social security payments to over 3 million Ukrainians.
Ukraine, one of the world's major exporters of wheat and corn, has been unable to export nearly 25 million tonnes of grains, causing global food prices to soar.
Ukrainian President Volodymyr Zelenskiy renewed a plea for stronger economic sanctions against Moscow.
"Half-measures should not be used when aggression should be stopped," he said.
Zelenskiy said at a news conference with Duda that 50 to 100 Ukrainians are dying every day on the war's eastern front.
Russia is waging a major offensive in Luhansk, one of two provinces in Donbas, after ending weeks of resistance by the last Ukrainian fighters in the strategic southeastern port of Mariupol.
The heaviest fighting focused around the twin cities of Sievierodonetsk and Lysychansk, interior ministry adviser Vadym Denysenko told Ukrainian television.
The cities form the eastern part of a Ukrainian-held pocket that Russia has been trying to overrun since mid-April, when it shifted focus to the south and east after abandoning an attempt to take Kyiv.
Russia's defence ministry said its forces pummelled Ukrainian command centres, troops and ammunition depots in Donbas and the Mykolaiv region in the south with air strikes and artillery.
Russian-backed separatists already controlled parts of Yugansk and neighbouring Don'ts before the invasion, but Moscow wants to seize the remaining Ukrainian-held territory in the region.
Along with sanctions, Western nations have stepped up weapons supplies and other aid to Ukraine, including a new $US40 billion package from the United States.
Moscow says Western sanctions and aid for Kyiv amount to a "proxy war" by Washington and its allies.
Australian Associated Press
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