President Volodymyr Zelenskyy said in a video that the Russian forces hit the city with two ballistic missiles, damaging a building of the Institute of Communications.
"I've received preliminary reports on the Russian strike on Poltava. According to currently available information, two ballistic missiles hit the territory of an educational institution and a nearby hospital," Zelenskyy said.
The death toll, as well as the number of wounded are likely to rise in the coming hours.
The attack will probably pile more pressure on Western countries to allow Ukraine to use their weapons to strike targets deep within Russia.
Ukraine has long complained that restrictions on the use of Western-made weapons limit its ability to defend itself while Russia is free to strike targets anywhere in Ukraine.
Videos posted on social media, reportedly from Poltava, showed buildings wrecked by explosions, and casualties lying on the ground.
Ukraine’s Interior Ministry said 11 people had been rescued from the rubble, and emergency services were searching for casualties in neighboring blocks of flats that had their windows blown in by the force of the blast.
Local authorities have also issued a plea for blood donors owing to the high number of casualties.
