Drones and missiles struck several high-rise apartment buildings and damaged electricity lines, leaving some 140,000 residents without power, according to Kyiv Mayor Vitali Klitschko.
The central Kyiv Pechersk Lavra monastery, a UNESCO World Heritage site founded in 1051, was seriously damaged in a direct attack, Tymur Tkachenko, the head of the capital's military administration, said in a separate Telegram post.
"A brutal assault on our people and our heritage. This is the true face of Russia's Orthodox values," Ukrainian Prime Minister Yulia Svyrydenko said on X, with her post showing the monastery buildings in flames.
As towering flames rose over the monastery, residents took shelter underground in the worst Russian missile attack on Ukraine since early June when drones and missiles killed more than 20 people and left more than 100 wounded.
Drones continue to attack Kyiv from different directions, Ukraine's Air Force said on Telegram, with explosions heard in the city, a Reuters witness said.
Neighbouring Poland, a European Union and a NATO member, has scrambled its fighter jets and put ground-based air defence systems and radar reconnaissance on a state of readiness, Poland's Armed Forces said in a post on X.
Most of Ukraine's territory was under air raid warnings in the early hours of Monday.
"What more must the Kremlin Antichrist do for the world to realize that decisive action must be taken so that the Russian terror against Ukraine and the very principles of peace comes to an end?" Metropolitan Epifaniy, head of the Orthodox Church of Ukraine, said on X.
Five emergency service rescues were killed and at least another five injured after a second Russian strike hit Kharkiv, Ukraine's second biggest city, Interior Minister Ihor Klymenko said on Telegram, with attacks also in the region of Dnipro, according to social media posts by local authorities.
Ukraine has recently intensified attacks on Russian industrial and energy facilities, as it tries to deprive Moscow from revenues to bring the end to the war closer.
On Monday, three people were killed and another three, including a one-year-old child, were injured in a drone attack on the Russian city of Tula, an industrial cluster south of Moscow, the regional governor said in a Telegram post.
Moscow was also repelling a drone attack overnight, its mayor said on social media.
The latest strikes come after Ukrainian President Volodymyr Zelenskiy said on Sunday he had spoken to US President Donald Trump and discussed efforts to achieve an end to the more than four-year war, ahead of a G7 meeting in France this week.
Trump told Russian President Vladimir Putin on Sunday that ending the conflict in Ukraine was vital and he was ready to help, the Kremlin said.
Progress towards a peace agreement in Ukraine has been slow, with US officials and mediators concentrating on the conflict in the Middle East.
with dpa