Search and rescue operations are ongoing at the sites of the strikes, the State Service for Emergencies said.
Ukrainian President Volodymyr Zelensky has met with visiting NATO secretary-general Mark Rutte to discuss Ukrainian and European security.
The men were said to have paid smugglers the equivalent of more than $3,600 each.
The UN Refugee Agency warned on Friday that aid was slowing down.
According to them, the battle for the strategically important city of Bakhmut continues.
UN secretary-general António Guterres wants to save an agreement on grain exports from Ukraine via the Black Sea, which Moscow suspended following drone attacks on its fleet.
“EU strongly condemns Russian missile strike on Odessa’s seaport,” top EU foreign affairs envoy, Josep Borrell, wrote on Twitter.
Ukraine provides 10 per cent of the world’s wheat, 14 per cent of the world’s corn, and 47 per cent of all sunflower oil on the planet.
A government report on Monday said the Russian leadership had agreed with Kyiv and Turkey on a scheme to release grain shipments from Odessa.
Footage circulated online shows Ukrainians and foreign nationals at ATMs, airports, and train stations trying to flee the country.
