Russian drones attacked Ukraine's Black Sea port city of Odesa early on Thursday, killing two people and injuring five more, in addition to sparking fires and damaging infrastructure, the regional governor said.

"The enemy attack damaged residential high-rises, private houses, a supermarket, a school, and cars," Oleh Kiper wrote on the Telegram messaging app. "Fires broke out in some places and are being extinguished by our rescuers."

Ukraine's state-owned railway Ukrzaliznytsia said the overnight attack also damaged its tracks, the contact network and three freight cars.

"Railway employees are carrying out rapid repair work to ensure that freight trains run to ports without interruption. They are currently following an alternative route."

Passenger trains were running on schedule, it added on Telegram. One of the people killed in his home during the attack on Odesa was a railway employee, according to the company.

Videos posted by Kiper showed heavily damaged facade of a high-rise building, a storefront with shattered windows and fire-fighters battling flames at one of the sites in the city.

In Kharkiv, Ukraine's second-largest city in the northeast, Mayor Ihor Terekhov said a drone had struck a petrol station in the city center, sparking a fire.

Terekhov provided no further details.