President Zelensky says Russia has started using "far more" ballistic missiles in its attacks on Ukraine.
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Drones, ballistic and cruise missiles targeted several locations in Ukraine, including Kyiv, Dnipro in the centre and Odesa in the south.
Air raid alerts in the capital lasted for most of the night. On Tuesday, sirens rang out again as Russian drones and cruise missiles approached the capital.
President Volodymyr Zelensky said a "significant number" of targets had been intercepted. But he also said that, in terms of air defence missile prices alone, repelling that attack had cost Ukraine about €80m (£69m).
Between Monday and Tuesday, at least four people died and 33 others were injured in strikes across Ukraine.
On Tuesday morning, more than 5,600 residential buildings – each with dozens of flats – in Kyiv woke up to no heating. A large part of the capital also has no water.
Mayor Vitalii Klitschko said almost 80% of those buildings had just had their heating restored following the large-scale attack on 9 January, which knocked out power for much of the city. Since then, relentless efforts by technicians had managed to reinstate electricity and gas for thousands - only for that work to be undone overnight.
"I have no electricity and no water," Oleksandr Palii, a 29-year-old veteran, told the BBC. "I didn't sleep until 3am because of the strikes either – there were explosions all night."
The Ukrainian president had been due to travel to the World Economic Forum in Davos, Switzerland, on Tuesday but, in the wake of the overnight strikes, he said he had decided to stay in Kyiv.
He would travel to Davos only if documents on security guarantees with the United States and a prosperity plan were ready to be signed, he added.
Temperatures have stayed well below freezing since the start of the year.
Ukrainian media has reported instances of radiators bur