Three civilians were killed and 17 wounded in a pre-dawn rocket strike on Thursday, the local emergency service said. That followed a Russian attack on Kharkiv on Wednesday, in which the emergencies service initially said 12 people were killed.
Governor Oleh Synehubov said more bodies had been discovered as rescuers picked their way through destroyed houses.
"As of now, 17 people have died in Kharkiv ... and 42 people have been injured," he wrote on Telegram, describing the attacks as "an act of terrorism".
Synehubov also said two people were killed on Thursday in a rocket attack on the town of Krasnohrad in the Kharkiv region.
President Volodymyr Zelenskiy described Wednesday's attack on Kharkiv, Ukraine's second-largest city, as a "devious and cynical strike on civilians with no justification".
"We cannot forgive. We will avenge it," he said.
Russia denies deliberately targeting civilians in what it calls a "special military operation" in Ukraine.
Kharkiv resident Tamara Kramarenko said the dormitory where she lived had been hit by a missile on Wednesday.
"Bang, grey. Grey fog ... we got three windows - nothing else left! The stairs started collapsing, people started helping each other," she told Reuters.
(Reporting by Aleksandar Vasovic, Max Hunder and David Ljunggren; Editing by Tom Hogue, Timothy Heritage, Alex Richardson and Daniel Wallis)
