Kyiv, Ukraine - Several Ukrainian cities were targeted by Russian attacks overnight, leaving two dead in Kherson on Thursday while falling debris from downed incoming missiles caused multiple injuries in the capital Kyiv.

"Since the beginning of the current day, the Russian occupiers have launched a massive missile attack on the civilian infrastructure of a number of regions," Ukraine's General Staff said.

Two men aged 29 and 41 were killed in an attack which hit a dormitory in the southern city of Kherson, the regional governor Oleksandr Prokudin said.

"The Russian army shelled the residential quarters of Kherson," he said on the messaging platform Telegram. "As of this hour, we know of two dead civilians... they were inside the dormitory."

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Four people were taken to hospital, Prokudin added, including a 61-year-old woman in a serious condition.

The strikes come as Ukrainian President Volodymyr Zelensky makes his second wartime visit to Washington in a bid to win fresh aid to fight Russian invaders despite signs of war fatigue among US lawmakers.

In Kyiv, falling debris from shot-down missiles resulted in seven people injured and damage to buildings, authorities said.

"According to initial reports, cruise missiles of the X-101/555/55 type were launched from about 10 Tu-95MS strategic aircraft," Sergiy Popko, head of the city's military administration, said on Telegram.

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"More than 20 enemy targets were destroyed by air defense forces and means."

"As a result of the downing of the missiles, debris fell in several areas of the capital."

Citing medics, Kyiv Mayor Vitali Klitschko said on Telegram that seven people were injured in the city's Darnytskyi district.

"Three of them are in city hospitals," he said, including a nine-year-old girl and an 18-year-old woman. Four others were treated at the scene.

Popko said the air alarm in Kyiv lasted more than two hours.

"The capital has already passed the mark of 1,000 hours of alerts since the start of the full-scale invasion," he said. "We survived it and will overcome a lot more together."

Interior Minister Igor Klymenko said a hotel was hit by a missile in the central city of Cherkasy, resulting in seven people being injured.

"We are looking for victims who may still be under the rubble," he said.

Sergiy Lysak, governor of the east-central Dnipropetrovsk region, said Nikopol city "came under attack," resulting in three people injured, while 11 houses and five commercial buildings were destroyed.

Kharkiv Mayor Igor Terekhov said two people were hospitalized "as a result of the morning shelling" of the eastern city, which is close to the Russian border.

He said on Telegram that there were "at least six strikes," all in the Slobidsky district.

Klymenko said a Kharkiv warehouse was destroyed.

Maksym Kozytskyi, governor of the western Lviv region, said three missiles struck industrial facilities in the city of Drogobych, destroying one warehouse and causing two blazes. No victims have been reported so far.

Klymenko said there were also "hits and damage" in the northwestern Rivne region.