Oleksandr Senkevych, mayor of the southern Mykolaiv region, which borders the vital Black Sea port city of Odessa, reported powerful explosions in the city.
“Stay in shelter!” he wrote on the Telegram messaging app when the air raid sirens sounded.
The cause of the explosions was not immediately clear, although Russia later said it hit army command posts in the area.
Reuters could not independently verify the battlefield reports.
Authorities said a rocket hit an apartment building near Odessa on Friday, killing at least 21 people. A shopping center was hit in the central city of Kremenchuk on Monday, killing at least 19.
Ukrainian President Volodymyr Zelenskyy denounced Friday’s attacks as “deliberate, deliberately targeted Russian terror and not as some kind of mistake or an accidental missile attack”.
In his overnight televised speech on Saturday, he said it would be a “very difficult road” to victory, but that it was necessary for Ukrainians to remain determined and inflict losses on the “aggressor” … so that every Russian remembers that Ukraine cannot be broken”.
“In many areas of the front there is a sense of easing, but the war is not over,” he said. “Unfortunately it is getting more intense in several places and we must not forget that. We have to help the army, help the volunteers, those who are now on their own.”
Kiev says Moscow has intensified rocket attacks on cities far from the main eastern battlefields and deliberately hit civilian sites. Ukrainian troops on the eastern front lines, meanwhile, describe intense artillery shelling that has ravaged residential areas.
Thousands of civilians have been killed and cities razed to the ground since Russia invaded Ukraine on February 24. Kremlin spokesman Dmitry Peskov echoed Russia’s denials that its troops are targeting civilians.
The Chief of the General Staff of the Russian Armed Forces, Valery Gerasimov, inspected Russian troops involved in what Moscow calls its “special military operation,” the Russian Defense Ministry said, although it was not clear whether he was in Ukraine.
The inspection followed slow but steady gains by Russian forces with the help of relentless artillery in eastern Ukraine, a focus for Moscow after it narrowed its broader war targets to overthrow the government following fierce Ukrainian resistance.
Russia is trying to expel Ukrainian troops from Luhansk and Donetsk provinces in the industrialized eastern Donbas region, where Moscow-backed separatists have been fighting Kiev since Russia’s first military intervention in Ukraine in 2014.
“They’re definitely trying to demoralize us. Maybe that bothers some people, but for us it just brings more hatred and determination,” said a Ukrainian soldier returning from Lysychansk.