The attack early on Wednesday killed two and injured four in the capital, Kyiv City Military Administration said on Telegram, and Mayor Vitali Klitschko said fires broke out, affecting private houses along with a store and a warehouse.
A Reuters witness heard explosions in the city.
Tymur Tkachenko, Kyiv regional governor, writing on Telegram, said that a Russian missile and a drone strike killed a child and injured three more people in the area, also damaging infrastructure facilities, houses, warehouses and cars.
Ukraine's neighbours, European Union and NATO members Romania and Poland, both scrambled military jets to protect their airspaces amid Russian attacks on Ukraine, according to defence ministry and armed forces statements on X.
A Ukrainian drone attack on the Russian Samara region, an oil producing and refining hub some 1100km southeast from Moscow, has damaged private houses, Governor Vyacheslav Fedorishchev said on social media platform VK.
Reuters could not immediately independently verify the reports.
Earlier Russian glide bombs struck homes and a school in the northern city of Sumy, killing two people and injuring six.
President Volodymyr Zelenskiy, speaking in his nightly video address on Tuesday, said one bomb struck a house, killing a woman. A second bomb hit the school.
"An ordinary school, where children happened to be at the time," he said.
"The building sustained considerable damage, but the children and teachers were in a shelter, and fortunately, thanks to that, no one was hurt at the school."
"Russian terrorists and simply unhinged scumbags. To strike at children, at schools, at ordinary homes like this. America, Europe, all our partners must not forget that Russia will not stop this madness without real pressure," he said.
"We expect steps in response to these strikes - and that they will go beyond lip service."
Governor Oleh Hryhorov, writing on Telegram, put the death toll at two, with three children among the injured. He said teachers and school officials had managed to evacuate 100 people into the shelter.
Zelenskiy said Belgium would transfer three F-16 fighter jets to Ukraine by the end of the year to help in its war with Russia.
"There is an important agreement with Belgium on the transfer of three F-16 fighter jets by the end of this year," he wrote on X. "
We will work to receive these aircraft through an accelerated procedure."
Ukraine had already received "urgent deliveries" of F-16 ammunition from Belgium and Spain, among other countries.
Zelenskiy said later that Ukraine had received delivery the day before of a "very good" assistance package of a NASAMS air defence system, developed jointly in the US and Norway.
Zelenskiy also said that talks were proceeding to ensure that Ukraine has a supply of missiles for the Patriot air defence system, which play a critical role in intercepting Russian ballistic missiles.
Zelenskiy said tests were continuing to improve the efficiency of Ukrainian interceptors against Russian jet-powered drones, which fly higher and faster than conventional drones.
Of more than 100 Russian drones deployed on Tuesday, he said, 29 were jet-powered and 18 of those had been downed.
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