Since turning away from Ukraine's capital, Russia is using massed artillery and armour to try to capture more territory in the Donbas, comprised of the Donetsk and Luhansk areas, which Moscow claims on behalf of separatists.
"The occupiers are trying to exert even more pressure. It is hell there - and that is not an exaggeration," Zelenskiy said in a late Thursday address.
"(There are) constant strikes on the Odesa region, on the cities of central Ukraine. The Donbas is completely destroyed."
Russian shelling in Luhansk has killed 13 civilians over the past 24 hours, regional governor Serhiy Gaidai said.
Twelve were killed in the town of Sievierodonesk, where a Russian assault had been unsuccessful, he said.
Ukraine's Prosecutor General's office said 232 children had been killed and 427 wounded since the beginning of the Russian invasion.
Moscow calls it a "special military operation" to rid Ukraine of fascists, an assertion Kyiv and its Western allies say is a baseless pretext for an unprovoked war.
Russia had intensified its offensive and assault operations in Donetsk, the General Staff of Ukraine's Armed Forces said.
Moscow denies targeting civilians.
The past week has seen Russia secure its biggest victory since the invasion began, with Kyiv announcing it had ordered its garrison in a steelworks in Mariupol to stand down, after a protracted siege of the city.
Russian forces have, however, been pushed back this month from the outskirts of the second-largest city Kharkiv. Ukraine says it has recaptured 23 settlements near Kharkiv in the past two weeks.
As the invasion nears the three-month mark, the US Senate overwhelmingly approved nearly $US40 billion ($A57 billion) in new aid for Ukraine, by far the largest US aid package to date.
The G7 also agreed to provide Ukraine with $US18.4 billion. Ukraine said the money would speed up victory over Russia and was just as important as "the weapons you provide".
US Treasury Secretary Janet Yellen told reporters: "The message was, 'We stand behind Ukraine. We're going to pull together with the resources that they need to get through this.'"
The United States also said it had authorised $US100 million in additional arms, equipment, and supplies for Ukraine.
And in a further sign of Western action hurting the Russian economy, five foreign vice-presidents of Russia's Rosneft resigned because of EU sanctions forbidding European citizens or Russians living in the EU to work at the oil company, sources said.
But Western divisions have also been on show, with NATO member Turkey opposed to Sweden and Finland joining the alliance, a move that would reverse generations of military non-alignment in the biggest European security shake-up in decades.
Ankara accuses the Nordic states of harbouring Kurdish militants, but US President Joe Biden and European leaders said they were confident Turkey's concerns could be addressed.
Biden, hosting Swedish Prime Minister Magdalena Andersson and Finnish President Sauli Niinisto at the White House, told reporters: "I think we're going to be OK."
Niinisto said Finland would commit to Turkey's security, adding, "We condemn terrorism in all its forms and we are actively engaged in combating it."
In Mariupol, the ultimate outcome of the bloodiest battle in Europe for decades has remained unclear, with uncertainty over the fate of hundreds of Ukrainian defenders.
Moscow said on Thursday that 1730 Ukrainian fighters had surrendered so far, including 771 in the past 24 hours.
Ukrainian officials, who have sought a prisoner swap, had declined to comment, saying it could endanger rescue efforts. Late on Thursday, Sviatoslav Palamar, deputy head of the Azov Regiment defending the steelworks, released a video in which he said he and other commanders were still on the territory of the plant.
The leader of Russian-backed separatists in control of the area said nearly half of the fighters remained inside the steelworks, where underground bunkers and tunnels had protected them from weeks of Russian bombardment.
The wounded were given medical treatment and those who were fit were taken to a penal colony and were being treated well, Denis Pushilin said.
