Air raid sirens could be heard across several regions of Ukraine early today including Luhansk, Kharkiv and Dnipro.
Serhiy Gaidai, the governor of Luhansk, said the region was attacked 22 times in the past 24 hours.
"During the day on May 9th, the Russians fired en masse on all possible routes out of the region."
In Moscow, during yesterday's annual parade - with the usual ballistic missiles and tanks rumbling across the cobblestones - Mr Putin told Russians they were again fighting "Nazis".
"You are fighting for the Motherland, for its future, so that no one forgets the lessons of World War Two. So that there is no place in the world for executioners, castigators and Nazis," Mr Putin said.
Ukraine's President Volodymyr Zelensky, in his own speech yesterday, promised Ukrainians would triumph.
"On the Day of Victory over Nazism, we are fighting for a new victory. The road to it is difficult, but we have no doubt that we will win," said Mr Zelensky.