Teams worked through the night to rescue some 362 people and pump water from buildings, the service said on the Telegram messaging app, and it posted pictures of passengers being lifted from a flooded bus and cars pulled from the water.
"A horrific situation in Odesa these days - 9 people have died as a result of the natural disaster, including a child," President Volodymyr Zelenskiy said on X platform.
He added that the whereabouts of one more person were still being verified.
A family of five who lived in lower ground floor flat of a building was unable to escape the wave of water, the emergency service's spokesperson for the Odesa region Maryna Averina told Ukrainian television.
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