Rescue workers from the State Emergency Service were already on the scene, desperately searching for survivors, when Denys Kliap arrived. They were pulling bodies from the rubble “without legs, others without arms, some even without heads,” he said.

Shattered glass was everywhere. Nearby buildings showed gaping holes where windows and doors had been blasted off.

Mr. Kliap, the 26-year-old director of Free and Unbreakable, a volunteer rapid response team in the eastern Ukrainian city of Poltava, had seen many such scenes of carnage. But the devastation of the strikes on Tuesday still shocked him.

“When we arrived, the only thing I remember was the pile of bodies scattered all over the territory of the institute,” he said.

Russian missile strikes on a military academy and a neighboring hospital in Poltava, about 100 miles from the Russian border, had residents scrambling to reach shelters on Tuesday, often unsuccessfully, with many reporting that sirens sounded only very shortly before the attacks.

President Volodymyr Zelensky said the strikes had been carried out with ballistic missiles, which can travel at supersonic speed and reach a target anywhere in Ukraine in a matter of minutes.