By Pavel Polityuk and Jonathan Landay
KYIV/KHARKIV, Ukraine (Reuters) - Buildings in Odesa lay in ruins on Tuesday, a day after Kremlin forces pounded the southern Ukrainian port with missiles and Russian President Vladimir Putin led defiant celebrations marking the Soviet's victory over Nazi Germany in World War Two.
While Putin was silent about plans for any escalation in Ukraine, there was no let up in fighting, with a renewed push by Russian forces on Monday to defeat the last Ukrainian troops holding out in a steelworks in ruined Mariupol.
"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," Putin said.
Ukraine's President Volodymyr Zelensky, in his own speech on Monday, 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 Zelensky.
In Odesa, the major Black Sea port for exporting agricultural products, one person was killed and five people were injured when seven missiles hit a shopping center and a depot, Ukraine's armed forces said on Facebook.
Video footage from the scene showed fire and rescue workers combing through piles of rubble dousing still smoking wreckage.
Ukraine - a major maize and wheat producer - and its allies have intensified efforts on how to unblock ports or provide alternate routes for exporting grain, wheat and corn.
European Council President Charles Michel visited Odesa on Monday, urging afterwards a global response to aid Ukraine.
A meeting between Michel and Ukrainian Prime Minister Denys Shmyhal in Odesa was interrupted by the missile attack, forcing the men into a bomb shelter, according to Shmyhal's official Twitter account.
In the town of Bogodukhov, northwest of Kharkiv, four people were killed and several homes were destroyed in Russian attacks, local media quoted Kharkiv officials as saying.
In some eastern regions of Ukraine, Luhansk, Kharkiv and Dnipro, air raid sirens could be heard early on Tuesday.
Ukraine's defense ministry said Russian forces backed by tanks and artillery were conducting "storming operations" at Mariupol's Azovstal plant, where hundreds of Ukrainian defenders have held out through months of siege.
Mariupol lies between the Crimean Peninsula, seized by Moscow in 2014, and parts of eastern Ukraine under the control of Russia-backed separatists. Capturing the city would allow Moscow to link the two areas.
More than 5.5 million Ukrainians have fled their country since Russia's invasion on February 24, according to the United Nations, which has called it Europe's fastest-growing refugee crisis since World War Two.
Moscow's gains from the invasion, however, have been slow at best and it has little to show for it beyond a strip of territory in the south and marginal gains in the east.
President Joe Biden said he was worried that Putin "doesn't have a way out right now, and I'm trying to figure out what we do about that".
Sources say Democratic lawmakers have agreed on a $40 billion aid proposal for Ukraine, including a massive new weapons package.
The White House had earlier described Putin's remarks during his Victory Day speech as "revisionist history that took the form of disinformation."
The Soviet victory in World War Two has acquired almost religious status in Russia under Putin, who has invoked the memory of the "Great Patriotic War" throughout what he calls a "special military operation" in Ukraine.
Western countries consider that a false analogy to justify unprovoked aggression.
"There can be no victory day, only dishonor and surely defeat in Ukraine," said British Defense Secretary Ben Wallace.
In Poland, the Russian ambassador was surrounded by protesters at a memorial ceremony and doused in red paint. Ambassador Sergei Andreyev, his face dripping and his shirt stained, said he was "proud of my country and my president".
Sheltering in a metro station in Kharkiv -- Ukraine's mainly Russian-speaking second city which has been bombed relentlessly since the war's first days -- World War Two survivor Vira Mykhailivna, 90, buried her tear-stained cheeks in her hands.
"I didn't think this could ever happen to us," she said. "This day was once a great celebration."
(Additional reporting by Oleksandr Kozhukhar in Lviv, Ronald Popeski in Winnipeg, Lidia Kelly in Melbourne and Reuters bureaus; writing by Rami Ayyub and Lincoln Feast; editing by Himani Sarkar)