The attacks on cities including Kyiv and Dnipro followed Russian warnings of "systematic" strikes on the capital after a deadly drone attack on a dormitory in Ukraine's Russian-held region of Luhansk in May that Kyiv denies carrying out.
It was the third heavy assault on Kyiv in under a month.
Russia has stepped up strikes on its neighbour, which it invaded in 2022, as Washington focuses on Iran and US-brokered talks on the war in Ukraine have stalled, with deadlock on the battlefield and Kyiv regularly hitting oil refineries in Russia.
Ukrainian President Volodymyr Zelenskiy said Russia had fired 73 missiles and more than 600 drones in the overnight attack and again urged Washington to send additional Patriot missile interceptors to replenish Kyiv's dwindling supplies.
"This was a large-scale attack and an absolutely clear statement from Russia: if Ukraine is not protected from ballistic and other missile strikes, these attacks will continue," Zelenskiy said on X on Tuesday.
The Kremlin said the war had entered "a new paradigm" after what it called "inhumane acts of terror" Ukraine's military against civilians.
Moscow warned of systemic strikes and urged foreigners to leave Kyiv.
Zelenskiy sent a letter to US President Donald Trump and Congress on May 27 asking for air defence systems, but officials say he has not received a response.
Moscow's war in Ukraine has killed tens of thousands of people, forced much of the population out of their homes and devastated cities, towns and villages, and Russia controls about one-fifth of Ukraine.
Ukraine has also hit civilian targets during attacks on Russia or Russian-occupied areas, though on a far smaller scale. Both sides deny targeting civilians.
Photographs on Tuesday showed large explosions and plumes of smoke billowing over high-rise buildings in Kyiv, where the overnight strikes killed six people and wounded more than 60, including three children, the capital's mayor said.
Twelve people were killed, including two young boys, in the southeastern city of Dnipro, where a four-storey apartment building had been partially destroyed, local officials said.
Kyiv was the main target of the attacks, officials said.
At least nine high-rise buildings, a kindergarten, a clinic, offices and administrative buildings were damaged.
Thousands took shelter in the Kyiv subway system, some carrying pets, belongings and mattresses.
Ukraine's air force said Russia launched 656 drones and 73 missiles, including 33 hard-to-shoot-down ballistic missiles and eight Zircon hypersonic missiles - which appeared to be the largest number of such missiles used during the war.
Air force units shot down or neutralised 40 missiles and 602 drones, but the air force did not list the Zircons among those that were intercepted.
Russia's defence ministry said it had carried out a "massive strike" on Ukraine's defence industry facilities using high-precision long-range weapons.
In Ukraine's northeastern region of Kharkiv, a child was among 14 people injured in the attacks, officials said.
NATO member Poland said it had scrambled military jets to secure its airspace after the Russian strikes on Ukraine.
Russian regions also came under attack.
The Ilsky oil refinery, in the southern Russian region of Krasnodar, caught fire after a drone attack, local authorities said on Telegram.
In Belgorod region bordering Ukraine, an 11-year-old boy was injured after a Ukrainian drone hit a home, local authorities said.
Russia downed 148 Ukrainian drones overnight, Russia's defence ministry said.
with DPA
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