The bombardment ignited a massive fire at a power station on Kharkiv’s western outskirts and killed at least one person.
President Volodymyr Zelensky denounced the “deliberate and cynical missile strikes” against civilian targets as acts of terrorism.
Ukraine’s second-largest city of Kharkiv appeared to be without power on Sunday night. Cars drove through darkened streets, and the few pedestrians used flashlights or mobile phones to light their way.
Separately, the Zaporizhzhia Nuclear Power Plant in the Russia-occupied south completely shut down in a bid to prevent a radiation disaster as fighting raged nearby.
Kyiv’s action in recent days to reclaim Russia-occupied areas in the Kharkiv region forced Moscow to withdraw its troops to prevent them from being surrounded, leaving behind significant numbers of weapons and munitions in a hasty flight as the war marked its 200th day on Sunday.
Ukraine’s military chief, Gen Valerii Zaluzhnyy, said its forces had recaptured about 1,160 square miles since the counteroffensive began in early September.
He said Ukrainian troops are only 30 miles from the Russian border.
One battalion shared a video of Ukrainian forces in front of a municipal building in Hoptivka, a village just over a mile from the border and about 12 miles north of Kharkiv.
Kharkiv Governor Oleh Syniehubov said Ukrainian troops have reclaimed control of more than 40 settlements in the region.
In Sunday night’s missile attacks by Russia, the Kharkiv and Donetsk regions seemed to bear the brunt. Dnipropetrovsk, Zaporizhzhia and Sumy had only partially lost power, Mr Zelensky said.
Kharkiv Mayor Igor Terekhov called the power outage “revenge by the Russian aggressor for the successes of our army at the front, in particular, in the Kharkiv region”.
Ukrainian officials said Russia hit Kharkiv TEC-5, the country’s second-biggest heat and power plant, and Mr Zelensky posted video of the Kharkiv power plant on fire.
“Russian terrorists remain terrorists and attack critical infrastructure. No military facilities, only the goal of leaving people without light and heat,” he tweeted.
But Zelenskiy remained defiant despite the attacks. Addressing Russia, he added: “Do you still think you can intimidate, break us, force us to make concessions? … Cold, hunger, darkness and thirst for us are not as scary and deadly as your `friendship and brotherhood.’ But history will put everything in place. And we will be with gas, lights, water and food … and WITHOUT you.”
Later in the evening, some power had been restored in some regions. None of the outages were believed to be related to the shutdown of the reactors at the Zaporizhzhia plant.
While most attention focused on the counter-offensive, Ukraine’s nuclear energy operator said the Zaporizhzhia nuclear power plant, Europe’s largest, was reconnected to Ukraine’s electricity grid, allowing engineers to shut down its last operational reactor to safeguard it amid the fighting.
The plant, one of the 10 biggest atomic power stations in the world, has been occupied by Russian forces since the early days of the war. Ukraine and Russia have traded blame for shelling around it.