Further east in the Dnipropetrovsk region, the governor reported an "enemy attack" and said rescue workers were searching for people under rubble in the city of Dnipro.
Ukraine said Russia had killed civilians deliberately in Kremenchuk. Moscow said it had struck a nearby arms depot and falsely claimed that the mall was empty.
Dnipropetrovsk regional governor Valentyn Reznychenko wrote on the Telegram app that Russia fired six missiles, three of which were shot down.
Railway infrastructure and an industrial enterprise had been destroyed and a services company was burning. Reuters could not independently verify the governor's account.
In the past two days, Ukrainians have described attacks by Russia in the southern region of Odesa and the city of Kharkiv in the northeast.
In Kharkiv, an early Russian target following its invasion in late February, authorities together with rescuers and volunteers of the Red Cross have restarted training for civilians on how to survive in the subways of a city being shelled, according to a Reuters photographer there.
The Western NATO military alliance, whose members have provided Ukraine with weapons to repel Russian advances, on Tuesday resolved a deadlock that paves the way for Finland and Sweden to become members. Turkey dropped its opposition to the Nordic countries joining NATO.
The development solidifies the alliance's response to Russia, particularly in the Baltic Sea, where Finnish and Swedish membership would give NATO military superiority.
At a NATO summit in Spain this week the alliance is expected to announce hundreds of thousands of troops shifting to a higher state of alert.
The attack in Kremenchuk drew a wave of global condemnation. Relatives of the missing were lined up at a hotel across the street from the wreckage of the shopping centre, where rescue workers had set up a base. Adults and children, some in tears, lit candles and laid flowers in a tribute to the dead.
Russia's defence ministry said its missiles had struck a nearby arms depot storing Western weapons, which exploded, causing the blaze that spread to the nearby mall.
Kyiv said there was no military target in the area.
Russia described the shopping centre as disused and empty. But that was contradicted by the relatives of the dead and missing, and the dozens of wounded survivors.
Meanwhile, Ukraine and Russia traded accusations at a UN Security Council meeting on Tuesday.
Ukrainian President Volodymyr Zelenskiy accused Russia of being a "terrorist state", prompting Russia to charge that he was using a Security Council address as a "remote PR campaign" to solicit more Western weapons.
Ukraine endured another tough day on the battlefields of the eastern Donbas region following last week's loss of the now-ruined city of Sievierodonetsk.
Russian forces are trying to storm Lysychansk, across the Siverskyi Donets River from Sievierodonetsk, to complete their capture of Luhansk, one of two eastern provinces Moscow aims to conquer on behalf of separatist proxies.
Western countries have imposed economic sanctions on Russia, but so far have failed to curtail Moscow's main source of income: oil and gas export revenue, which has actually increased as the threat of supply disruption has driven up global prices.
At the end of its annual summit, the G7 announced a new approach - leaving Russian oil on the market while imposing a cap on the price countries could pay for it.
The United States also imposed sanctions on more than 100 new targets and banned new imports of Russian gold, acting on commitments made by the G7.
