Several regions of Ukraine, including the capital Kyiv, were rocked by explosions on Saturday morning.
Officials said that Russian missiles were targeted on infrastructure.
In the east-central city of Dnipro, a Russian missile attack killed 12 people and wounded 64, including six children, regional governor Valentyn Reznichenko said.
Rescue teams toiled through the night in freezing temperatures in the aftermath of the Dnipro attack, with local officials saying people were still alive underneath the massive pile of wreckage.
"They keep sending SMS-es," Mikhailo Lysenko, deputy mayor of Dnipro said in a social media video. "We stop our work now and then to keep silence and we hear people scream from underneath the rubble."
President Volodymyr Zelenskyy said the number of those killed in the Dnipro apartment attack was likely to rise and he issued a fresh appeal to his Western allies for more weaponry to end "Russian terror" and attacks on civilian targets.
US Ambassador to Ukraine Bridget Brink and Kyiv's other allies condemned Saturday's Russian attacks.
"More security assistance is coming to help Ukraine defend itself," Brink said on Twitter, calling the strike on Dnipro "horrifying."
Critical infrastructure in parts of Ukraine, from Kharkiv in the east to Lviv in the far west, were damaged, according to local authorities.
Kyiv mayor Vitali Klitschko reported explosions in the city's Dniprovskiy district and urged residents to stay in shelters.
He said that fragments of a rocket fell in Golosiivskiy district, but no casualties were reported.
Oleg Synegubov, governor of the north-eastern Kharkiv region, said that “the enemy launched another missile attack on critical infrastructure and industrial facilities.”
There could be emergency power cuts in Kharkiv, the second largest city in Ukraine, and in the surrounding region, Mr Synegubov said.
Attacks were also reported in the southern Zaporizhzhia region.
Infrastructure targeting
The Russian military's campaign of attrition has been hitting Ukrainian infrastructure, causing blackouts and disruption to power and water as the winter bites.
The strikes on Saturday came as Ukrainian forces battled to defend the salt-mining town of Soledar in eastern Ukraine, the focus of a heavy Russian assault.
Russia said on Friday that its forces had taken control of Soledar. Kyiv said its troops were still fighting in the town.
