Austrian leader Karl Nehammer planned to meet Russian President Vladimir Putin in Moscow on Monday and will call for an end to the conflict. It would be Putin's first face-to-face meeting with a European Union leader since Russia's invasion started on February 24.
Russian forces were also pushing their offensive to establish control over the southern port city of Mariupol, a key target whose capture would link areas of Russian control to the west and east.
The Russian invasion has left a trail of death of destruction that has drawn condemnation from Western countries and triggered concern about Putin's broader ambitions.
About a quarter of Ukraine's 44 million population have been forced from their homes, cities turned into rubble, and thousands of people have been killed or injured - many of them civilians.
Russian forces have abandoned their attempt to capture the capital Kyiv but are redoubling their efforts in Ukraine's east. Britain's defence ministry said Russian shelling continued in the Donetsk and Luhansk regions.
Ukrainian forces had beaten back several assaults and destroyed Russian tanks, vehicles and artillery equipment, it said in its regular intelligence bulletin.
Britain also said Russia's continued reliance on unguided bombs greatly increased the risk of further civilian casualties.
Powerful explosions rocked cities in the south and east and air raid sirens blared out across Ukraine early on Monday.
Zelenskiy kept up his tireless campaign to generate international support and rally his countrymen, warning the coming week would be important and tense.
"Russian troops will move to even larger operations in the east of our state. They may use even more missiles against us, even more air bombs. But we are preparing for their actions. We will answer," he said in a late-night video address.
The general staff of Ukraine's armed forces said it was likely the Russians would try to disrupt supply lines and strike at transport infrastructure.
Russia's defence ministry said high-precision missiles had destroyed the headquarters of Ukraine's Dnipro battalion in the town of Zvonetsky.
Austrian Chancellor Karl Nehammer said he would meet Putin on Monday in Moscow.
"We are militarily neutral, but (have) a clear position on the Russian war of aggression against #Ukraine," Nehammer wrote on Twitter.
"It must stop! It needs humanitarian corridors, ceasefire & full investigation of war crimes."
Since Russia invaded, Zelenskiy has appealed to Western powers to provide more defence help, and to punish Moscow with tougher sanctions including embargoes on its energy exports.
Zelenskiy said he had confidence in his own armed forces but "unfortunately I don't have the confidence that we will be receiving everything we need" from the United States.
Mounting civilian casualties have triggered widespread international condemnation and new sanctions.
Moscow has rejected accusations of war crimes by Ukraine and Western countries. It has repeatedly denied targeting civilians in what it calls a "special operation" to demilitarise and "denazify" its southern neighbour.
Ukraine and Western nations have dismissed this as a baseless pretext for war.
French bank Societe Generale became the latest company to retreat from Russia, agreeing to sell its stake in Rosbank and the Russian lender's insurance subsidiaries to Interros Capital, a firm linked to billionaire Vladimir Potanin.
The World Bank on Sunday forecast the war would cause Ukraine's economic output to collapse by 45 per cent this year, with half of its businesses shuttered, grain exports mostly cut off by Russia's naval blockade and destruction rendering economic activity impossible in many areas.
The bank forecast Russia's GDP would contract by 11.2 per cent this year due to punishing Western sanctions.
