In Kyiv, Mayor Vitali Klitschko said two people, including the child, had died. In the southeastern city of Dnipro, where Russian attacks set residential buildings ablaze, the regional governor said one person was killed.
"At result of the enemy attack on the capital, two people have been killed, a 12-year-old boy and a 35-year-old woman," Klitschko wrote on Telegram on Thursday.
"Ten residents have been injured. Six are being treated in hospital."
Tymur Tkachenko, head of the capital's military administration put the injury toll in the city at 18, including a child.
An air raid alert remained in effect in both Kyiv and Dnipro more than two hours after it had been imposed in the capital.
Photos posted on line showed fires burning out of control and smoke billowing skyward.
Klitschko said rescue teams had rescued a mother and child from a building in a central district where the ground floor was badly damaged. He also said a missile had hit the sixth floor of an apartment building in the central Podil district.
Klitschko said a large fire had broken out in a building in a district in the north of the capital and four emergency medical workers were injured, while debris had fallen in several locations.
In Dnipro,Regional Governor Oleksandr Ganzha wrote on Telegram that one resident had died. He listed 10 people as injured and posted pictures showing residential buildings ablaze. In Kharkiv, Ukraine's second largest city in the northeast, officials said two people had been injured in drone strikes.
Meanwhile, the European Union expects to disburse 2.5 to 2.7 billion euros ($A4.1 to $A4.4 billion) to Ukraine after its parliament completed necessary reforms last week, Marta Kos, the EU's enlargement commissioner, said on Thursday.
Kos, speaking at an event in Washington together with Ukrainian Finance Minister Serhiy Marchenko, said the EU would definitely deliver a loan of 90 billion euros ($A148 billion) to Ukraine following the Hungarian election that swept Prime Minister Viktor Orban from power.
Marchenko told the event that Ukraine's financing gap of $US52 billion ($A73 billion) in 2026 will be covered once the EU loan became available, but said his government was still in discussions about closing the expected gap in 2027.
Kos said the disbursement would come from the EU's Ukraine facility, which is separate from the 90 billion euro ($A148 billion) loan.
"There is a Ukraine plan, where we have 173 reforms they have to do ... and if they deliver, we can give them the money," Kos told Reuters after the event, which took place during the International Monetary Fund and World Bank spring meetings in the US capital.
She welcomed the recent election results in Hungary, which had blocked the much larger EU loan to Ukraine.
"The chances that Ukraine will get the 90 billion euro loan are 100 per cent and we are already in contact," Kos told the event.
"Our president was speaking to the future, possible new prime minister of Hungary, Peter Magyar, and I think that we will be able to make this (happen) very soon."
"I am very happy because finally I can deliver, the European Union can deliver what we promised. Sometimes it takes time, yes indeed. But what we promise we deliver."
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