At least 34 people have been killed and 117 injured, including 15 children, after a Russian attack on the centre of Sumy, according to Ukrainian authorities.

Two Iskander-variant ballistic missiles struck at around 10:15 local time, both hitting the area around Sumy State University and its congress centre.

Images and videos of the aftermath show bloodied bodies scattered in the streets around the impact of the missiles. At least two children were killed.

Ukrainian President Volodymyr Zelensky said among the injured was a girl born this year, adding that medics were doing "everything they can" to save as many lives as possible.

"The strike hit right in the heart of the city on Palm Sunday," he said in his evening video message. "Only completely deranged scum can do something like this."

Moscow has not yet publicly commented on the attack.

Ukrainian authorities said that 20 buildings were damaged, including four educational institutions, as well as cafes, shops and five apartment buildings. Ten cars and trams were also hit.

Zelensky called for a "tough" response from other nations, adding that "talks have never stopped ballistic missiles and air bombs".

"Russia wants exactly this kind of terror and is dragging out this war. Without pressure on the aggressor, peace is impossible," he said.

The university's congress centre is often used for children's classes, with local residents saying that the space is an "educational hub for the entire city" and "very actively rented out for various courses, clubs, and master classes".

Officials in Sumy have said that the missiles were packed with cluster munitions, which can kill indiscriminately over a wide area.

They have caused burning vehicles and bent trees where the deaths seem to have been concentrated.

Nataliia, who gave only her first name, had been taking her child and other children to a shelter when the second strike hit her car.

"If we hadn't moved to the shelter on time we would have been in the car and we would be dead," she said.