Neighbouring Poland scrambled jets to secure its airspace in the wake of the barrage, after NATO accused Moscow of being behind a series of violations of the defence alliance's airspace.
Diplomatic efforts to stop the war have faltered and Russia has vowed to press on with the offensive that it launched in February 2022.
"Moscow wants to continue fighting and killing and deserves only the harshest pressure from the world," Ukrainian President Volodymyr Zelensky said following the strikes.
Following the massive aerial barrage, Zelensky held a round of calls with allies, including NATO chief Mark Rutte, Finnish President Alexander Stubb and Norwegian Prime Minister Jonas Gahr Store.
Russia said it had only hit military targets during the attack.
Ukraine's foreign ministry said that apart from residential buildings, a cardiology centre and a kindergarten had been among the buildings hit across the country.
- Scores of wounded -
The Ukrainian military said the country had been targeted by 595 drones and 48 missiles, most of which were shot down by air defences. But 31 drones and five missiles got through.
Zelensky said that energy sites were hit, accusing Russia of wanting to cause massive blackouts across Ukraine.
Ukrainian intelligence indicated that Russian oil tankers had been used as platforms to launch and guide the attack drones, he added.
Russia's full-scale invasion has ravaged swathes of eastern and southern Ukraine, killing tens of thousands of soldiers and civilians.
The Ukrainian leader vowed his country would target Russia's ability to fund the war and force Moscow to the negotiating table.
As well as the four people killed in Kyiv, the authorities said scores of people had been wounded across the Zaporizhzhia, Odesa, Sumy, Cherkasy and Mykolaiv regions.
Ivan Fedrorov, the governor of Zaporizhzhia, where a big nuclear plant is under Russian control, said the main city of the region had been hit "at least four times" and 42 people had been wounded.
- 'In shock' -
Kyiv region resident Mark Sergeev and his family had been sleeping when a missile hit their apartment in the middle of the night.
"I still can't believe that the children are alive," the 35-year-old told AFP. "It's such a blessing from God.
"They were right under the roof when it hit them. The roof was torn off right above my eldest son's bed," he added.
Anna, a 26-year-old resident who did not give her last name, said her flat had been covered in broken glass after being hit.
"I was in shock, so I didn't hear much...," she said.
"But I heard a rocket flying for a long time, and then there was just an explosion and the windows shattered."
Zelensky posted photos of residential buildings in flames, with emergency services putting out fires and rescuing people from shattered buildings.
More victims could be uncovered in the debris, rescuers said. AFP reporters saw rescuers using heavy machinery to clear rubble from near-destroyed buildings.
- Poland scrambles jets -
Poland's armed forces said on X that Warsaw had scrambled fighter jets in its airspace and put ground-based air-defence systems on high alert.
In recent weeks, several European countries have accused Russia of violating their airspace with drones and fighter jets, in what NATO sees as a test of its resolve.
Russia has denied that it is responsible for the incursions or that it plans to attack any NATO nation.
In an address at the UN General Assembly in New York on Saturday, Moscow's Foreign Minister Sergei Lavrov warned that "any aggression against my country will be met with a decisive response".
Zelensky said on Saturday that Ukraine had received a US-made Patriot air-defence system from Israel, and two more were expected to arrive soon. He was speaking after returning from New York, where he also addressed the UN.
Kyiv and Moscow also said on Saturday that the Russian-occupied Zaporizhzhia nuclear power plant -- Europe's largest -- had been off the grid for four days, stoking fears of a potential nuclear incident.
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