Watch: Russian aggression after explosion on Poland-Ukraine border kills two

Missiles rained down on cities including the capital Kyiv, Lviv and Rivne in the west, Kharkiv in the northeast, Kryvyi Rih and Poltava in the centre, Odesa and Mikolaiv in the south and Zhytomyr in the north.

A body was pulled out of a residential building that was hit and set ablaze in central Kyiv, and a senior presidential official said the power situation was "critical" after heavy damage to energy infrastructure.

In a video posted online, President Volodymyr Zelenskiy warned Ukrainians that more missile strikes were possible but added: "We are working, we will restore everything, we will survive."

Power was knocked out in areas of several cities including Kyiv, Lviv and Kharkiv, and the national grid operator announced emergency electricity outages in northern and central regions, and in Kyiv.

Kyiv's mayor said half of the capital was without electricity. The mayor of Lviv said 80 per cent of the city had no electricity so lighting, water and heating supplies were off. City authorities in Vinnytsia in west-central Ukraine were told to stock up on water following damage to a pumping station.

"This is the most massive shelling of the power system since the beginning of the war," Energy Minister German Galushchenko said.

Air force spokesperson Yuiy Ihnat said more than 100 missiles had been fired at Ukraine, surpassing the 84 fired by Russia on October 10 in what was previously the heaviest air strikes.

The country's biggest mobile phone provider warned of possible signal outages, and the transport system suffered disruptions in several areas.

In the capital, a five-storey apartment block was left smouldering after being hit by what residents said appeared to be shot-down missile parts.

Rescue workers and medics were quickly on the scene.

"I was in the apartment during the air raid warning. I saw a bright light in my window, and understood that something was coming. Then I heard the sound, as it was nearing," said Oleksandra, 22, who lives in the apartment block.

"I saw from my window as the rocket was flying, a bright fire, and the sound of something flying very close by. I immediately went outside... I saw people were running out of our building and that there was smoke.

"The last flat I lived in was also hit," she added. "Thankfully I was abroad at the time."

The attacks followed days after a humiliating retreat by Russian forces from the southern city of Kherson and coincided with a summit of the Group of 20 nations in Bali that was dominated by discussion of the war Ukraine.

"This is what Russia has to say on the issue of peace talks," Foreign Minister Dmytro Kuleba wrote on Twitter.

"Stop proposing Ukraine to accept Russian ultimatums! This terror can only be stopped with the strength of our weapons & principles."

Australian Associated Press