The strike, which killed at least 18 people in the central city of Kremenchuk, came as leaders from the Group of Seven nations met in Europe.
It was part of unusually intense barrage of Russian fire all across Ukraine, including in the capital of Kyiv, that drew new attention to a war that some fear could fade from the headlines as it drags on.
Speaking at the end of the G-7 summit in Germany, French President Emmanuel Macron appeared to address that concern, vowing that the seven leading industrialized democracies would support Ukraine and maintain sanctions against Russia ``as long as necessary, and with the necessary intensity.''
``Russia cannot and should not win,'' he said. He called Monday's attack on the mall ``a new war crime.''
As they have in other attacks, Russian authorities claimed that the shopping center was not the target.
How to counter Russia and back Ukraine will be the focus of a summit this week of the western NATO alliance, whose support has been critical to Kyiv's ability to fend off Moscow's larger and better equipped forces.
Ukrainian leaders, however, say they need more and better weapons if they are to continue to hold off and even drive back Russia, which is pressing an all-out assault in Ukraine's eastern region of the Donbas.
As Macron spoke, rescuers combed through the charred rubble of the shopping mall that authorities said was struck when more than 1,000 afternoon shoppers and workers were inside.
Kateryna Romashyna, a local resident, told The Associated Press that she had just arrived at the mall when there was an explosion.
The blast knocked her down. When another came about 10 minutes later, she realized she needed to get away.
``I ran away from the epicenter with all of my strength,'' she said. Fighting back tears, she added: ``You have to be a real monster'' to strike a shopping mall.
Many of those inside quickly fled the building when an air raid siren sounded and took shelter across the street, Ukrainian Interior Minister Denis Monastyrsky said.
Several of the bodies of those who didn't make it out in time are burned beyond recognition and their identification could take days, he said.
In addition to the 18 killed, authorities said 59 were wounded. Another 21 people are still missing, Monastyrsky said.
The attack recalled strikes earlier in the war that hit a theater, a train station, and a hospital. Ukrainian President Volodymyr Zelenskyy called it ``one of the most daring terrorist attacks in European history,'' while the G-7 leaders said ``indiscriminate attacks on innocent civilians constitute a war crime.''
At Ukraine's request, the UN Security Council scheduled an emergency meeting in New York on Tuesday to discuss the attack.
As condemnation of the strike came in from many quarters, Kremlin spokesman Dmitry Peskov struck a defiant note, saying Russia would press its offensive until it fulfills its goals.
He said the hostilities could stop ``before the end of the day'' if Ukraine were to surrender and meet Russia's demands, including recognizing its control over territory it has taken by force.
Russian Defense Ministry spokesman Lt. Gen. Igor Konashenkov claimed that warplanes fired precision-guided missiles at a depot that contained Western weapons and ammunition, which detonated and set the mall on fire.
Ukrainian authorities said in addition to the direct hit on the mall, a factory was also struck, but denied that any weapons were there.
Konashenkov also alleged that the mall was not in use, a false claim contradicted by witnesses.
One survivor, Oleksandr, an employee at the mall, told the AP from a hospital bed that the shopping center was packed with customers. He recalled stepping outside with a colleague for a cigarette, when the air raid siren went off.
``There was a black tunnel, smoke, fire,`` he said. ``I started to crawl. I saw the sun up there, and my brain was telling me I need to save myself.''
Ukraine's prosecutor general, Iryna Venediktova, said the missile attack was one of Russia's ``crimes against humanity,'' noting that Moscow's military has been ``systematically shelling civilian infrastructure with the aim to scare people, to kill people, to bring terror to our cities and villages.''
Venediktova emphasized the need for Ukrainians across the entire country to remain alert, adding that they should expect a similar strike ``every minute.''
On Tuesday, Russian forces struck the Black Sea city of Ochakiv, damaging apartment buildings and killing two, including a 6-year-old child.
A further six people, four of them children, were wounded. One of them, a 3-month-old baby, is in a coma, according to local officials.
The unusually intense spate of fire in recent days came as the G-7 leaders gathered in Europe. They pledged continued support for Ukraine and the world's major economies prepared new sanctions against Russia, including a price cap on oil and higher tariffs on goods.
Zelenskyy has called for more air defense systems from his Western allies to help his forces fight back. NATO's support for Ukraine will be a major focus of its summit as the alliance turns its attention once again to confronting an adversarial Russia.
Russian Foreign Minister Sergey Lavrov warned the West that ``the more weapons are pumped into Ukraine, the longer the conflict will continue and the longer the agony of the Nazi regime backed by Western capitals will last.''
Russia has falsely called the war a campaign to ``de-Nazify'' Ukraine, a country with a democratically elected Jewish president who wants closer ties with the West.
In a sinister message to NATO leaders who gathered in Madrid ahead of that summit, Russia's state space corporation Roscosmos published satellite images and the precise coordinates of the conference hall where the meeting will be held.
It also posted images and the coordinates of the White House, the Pentagon and the government headquarters in London, Paris and Berlin, referring to them as ``decision-making centers supporting the Ukrainian nationalists`` in a message on the Telegram app.
That wording echoes Russian President Vladimir Putin's earlier warnings that he could target such centers in response to what he has called Western aggression.