Tymur Tkachenko, the head of the capital's military administration, said debris from falling drones had struck buildings in different districts of the city, including residential buildings.
Unofficial Telegram channels posted videos of parts of apartment buildings ablaze on Thursday. There were no immediate reports of casualties.
Ukraine's air force also said Russian missiles had targeted other regions in the country, including Kharkiv, Sumy and Chernihiv in northern Ukraine and the central region of Poltava.
It follows a massive daytime Russian drone attack on Ukraine on Wednesday that targeted critical infrastructure in the west, killing at least six people and prompting NATO-member Poland to scramble fighter jets.
Hungary condemned the strikes on areas of Ukraine with ethnic Hungarian communities and summoned the Russian ambassador.
Ukrainian President Volodymyr Zelenskiy praised the Hungarian action as an "important message".
Zelenskiy, writing on Telegram while attending a security conference in Romania, said the Russian attack continued through Wednesday evening, with Moscow deploying missiles.
Zelenskiy had earlier said that since midnight, Moscow had launched at least 800 drones, with the attack deliberately targeting regions closest to the borders of NATO countries.
"It certainly cannot be called a coincidence that one of the longest massive Russian attacks against Ukraine takes place precisely at the time when the President of the United States arrived for a visit to China," Zelenskiy said on Telegram.
Zelenskiy said six people were killed and dozens injured in the attack, which spanned other regions. Ukraine's railway infrastructure was struck 23 times during the barrage, a presidential advisor said, though traffic was maintained.
A late Wednesday evening statement issued by Ukraine's military said 187 combat clashes had been recorded over 24 hours along the 1200-kilometre front line, with 55 air strikes and 178 guided bombs deployed by Russian forces.
The heaviest fighting occurred near Pokrovsk in the east, under Russian attack for many months, with 24 clashes recorded, and near Huliaipole further south, with 22 Russian attacks.
Wednesday's drone strikes were the first such major attack after a three-day US-brokered ceasefire between Ukraine and Russia, which ended on Monday.
Poland scrambled fighter jets as a preventative measure due to the Russian air strikes on Ukraine, the Polish army said.
Hungarian Prime Minister Peter Magyar, speaking after the new government's first cabinet meeting, said the Russian ambassador had been summoned to the foreign ministry on Thursday morning to meet Foreign Minister Anita Orban.
Ukraine's HUR military intelligence said the drone assault was designed to overwhelm Ukrainian air defences, warning of subsequent missile strikes.
It said Moscow targeted critical infrastructure and essential services in major cities.
Ukraine's air force said Russia had used the territory of Belarus and Moldova to fly the drones towards Ukraine.
State-owned oil and gas company Naftogaz said that Russian strikes had damaged two of its facilities in the northeastern region of Kharkiv and in Zhytomyr region, west of Kyiv. Governors and mayors reported strikes across western Ukraine.
Three people were killed and another six wounded in the northwestern region of Rivne.
An attack on a critical infrastructure facility in Zhovkva left the western town without power. There was also a strike on a residential building in the western city of Ivano-Frankivsk, local officials said.
The regional governor of Ukraine's far-west Zakarpattia region said the attack was the heaviest since the start of Russia's full-scale invasion in 2022.
Serhiy Beskrestnov, an adviser to the defence minister, said the barrage highlighted Moscow's evolving use of drones.
This time, drones were moving along between 5km and 10km from the Belarus border to overwhelm Ukraine's air defences and to get through to the western regions, he said.
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