Pictures posted online by regional governor Vadym Filashkin showed teams sifting through piles of smouldering rubble in the dark as well as a burned-out vehicle.
Filashkin told Ukrainian television that Russian forces at about 3 pm engaged in "mass shelling" of Pokrovsk with S-300 missiles."
"As a result of this barbaric attack, 11 people died, including five children aged from three to 17 years," he said.
"Ten people were injured. Rescue operations are continuing. Closer to morning we will have a better understanding of the final numbers of those who were injured."
Russian forces, Filashkin said, were "trying to inflict as much grief as possible on our land."
President Volodymyr Zelenskiy, in his nightly video address, said Russian must be made to feel the consequences of every such attack.
Ukraine President Volodymyr Zelenskiy accused Russia of targetting "ordinary, private homes". (AP PHOTO)
"The Russian strike quite simply targeted ordinary, private homes," Zelenskiy said.
"And Russia must be made to feel that none of these strikes will pass without consequences for the terrorist state."
Denise Brown, the UN's humanitarian coordinator for Ukraine, said she was truly horrified by the strikes and, particularly, the deaths of children.
Recent Russian attacks on towns, she said, were "leaving behind an outrageous number of children. Women and men killed and injured and a trail of loss and destruction".
There was no immediate response to a request for comment from Russia's Defence Ministry.
A Russian military statement issued earlier on Saturday said its forces had struck a command post used by a Ukrainian military formation near Pokrovsk, referring to the town by its Soviet-era name Krasnoarmeisk.
And a senior Moscow official working in Russian-occupied areas of Ukraine, Rodion Miroshnik, said Ukrainian forces had shelled a hospital in Donetsk, injuring three patients.
Russia denies targeting civilians in the war launched with the invasion of Ukraine in February 2022.
But its forces in the past two weeks have intensified attacks on Ukrainian cities and towns.
Ukraine has retaliated with strikes on targets in the Black Sea and on some Russian border areas, including missile and drone attacks that killed 25 people in the city of Belgrade this week.
The governor of Ukraine's Dnipropetrovsk region, adjacent to Donetsk, said one person was killed in drone strikes near the town of Nikopol, a frequent Russian target on the opposite bank of the Dnipro River from the Russian-held Zaporizhzhia nuclear power plant.
And officials said three people were injured in Russian shelling of areas of Kherson region to the southwest.
Rescuers searched for survivors at the site of a missile attack in eastern Ukraine. (EPA PHOTO)
