Kyiv Mayor Vitali Klitschko warned on Thursday that Russia has attacked key infrastructure in Ukraine as presidential adviser Mykhailo Podolyak said more than 120 missiles were launched at civilian centres.
Missile strikes and Ukrainian defensive fire was heard in the capital and there were blasts in the cities of Kharkiv, Odesa, Lviv and Zhytomyr.
Mr Klitschko said Kyiv may experience problems with power supply and urged residents to charge their mobile phones and stock up on water.
The attacks came as the country's spy chief Kyrylo Budanov told the BBC that the conflict was on the brink of stalemate.
"The situation is just stuck. It doesn't move," he said.
"We can't defeat them in all directions comprehensively. Neither can they.
"We're very much looking forward to new weapons supplies, and to the arrival of more advanced weapons."
Kharkiv Mayor Ihor Terekhov said officials were clarifying what had been hit in the strikes and whether there were any casualties.
"Two private houses in Darnytskyi district were damaged by the fragments of downed missiles," the Kyiv city military administration said on Telegram.
It said a business and a playground were also damaged and the situation of the victims "is being clarified".
Lviv Mayor Andriy Sadovyi said on Telegram that 90 per cent of the city was without electricity and electric public transport was not running.
"There may be interruptions in water supply," he said.
Russian President Vladimir Putin recently admitted that the country's troops had been hitting Ukraine's critical energy facilities.
That came after some international leaders, including French President Emmanuel Macron, said that targeting energy facilities could amount to a war crime.
Western intelligence has said that Russia is struggling to meet the ordnance needs for the invasion, but Moscow has refuted this.
"We will never run out of Kalibrs," the Russian Defence Ministry said on messaging app Telegram, referring to the cruise missiles used to batter Ukraine.