Ukraine asked for global support against the Russian invasion after an airstrike on Sunday killed at least 10 people, including three children.
President Volodymyr Zelenskyy called for the world to help Kyiv defeat "Russian evil."
A Russian drone hit an apartment block in the southern port city early Saturday morning, partially destroying several floors and leaving more than a dozen under the rubble.
"So far, 10 people have died, including three children: Mark, who was not even 3 years old, Yelyzaveta, 8 months old, and Timofey, 4 months old. Ukrainian children are Russia's military targets," Zelenskyyy said Sunday in a post on Telegram.
Local officials said they expect the toll to rise as there are still people unaccounted for.
Zelenskyy on Saturday had pleaded with Kyiv's Western allies to supply more air defense systems as Russia continues to pound his country with drones, missiles and artillery fire in the war's third year.
Ukraine is currently on the back foot with Russia having made recent frontline battlefield gains.
Ukraine's Interior Ministry separately reported one death and three people wounded in the southern Kherson region.
Zelenskyy said 215 emergency responders had taken part in an ongoing search and rescue operation in Odesa.
As delays to a crucial $60-billion aid package from the United States have left Kyiv facing ammunition shortages, Zelenskyy said the attack showed the importance of supporting Ukraine.
"We must win this war," he said Sunday.
"Every Russian loss at the front is our country's response to Russian terror. The world must respond to every manifestation of Russian evil and repel Russia's actions."
There was no comment on the strike in Moscow, which denies targeting civilians despite excessive evidence of Russian strikes on residential areas and the United Nations has verified at least 10,000 civilian deaths since Russia invaded in February 2022.
Ukraine's emergency services said they had found the bodies of families huddled together as they sifted through the rubble Sunday.
"A mother tried to cover her 8-month-old baby with her body. They were found in a tight embrace," the agency said on Telegram.
Russian military bloggers also reported an attempted massive Ukrainian drone attack on the annexed peninsula of Crimea overnight.
Moscow said it shot down 38 Ukrainian drones, while the Rybar Telegram channel, close to Russia's armed forces, said one hit a pipeline at an oil depot that was the presumed target of the attack.
Kyiv has hit several Russian oil facilities in recent months in what it has called fair retribution for Moscow's attacks on Ukraine's power grid.
A senior Ukrainian commander separately accused Russian forces of dropping explosives containing an unspecified chemical substance over the battlefield, and said the situation on the frontlines was "complicated but under control."
