Ukrainian President Volodymyr Zelensky praised the only survivor of a military plane crash as the death toll climbed to 26, after another cadet died and three more bodies were found.

Mr Zelensky went to the scene of the tragedy near the northeastern city of Kharkiv where an Antonov An-26 transport plane carrying 20 air force cadets and seven officers crashed during a training flight on Friday evening.

"Ukraine has lost 26 worthy sons," he said on Facebook, referring to the cadets and officers of the Kharkiv National Air Force University. "It is difficult to find words to express the pain of this loss," he said.

The plane burst into flames on landing near a highway around 2km from the Chuguiv military air base.  

President Zelensky visited the only remaining survivor in a military hospital in Kharkiv, posting a picture of the 20-year-old cadet lying in bed with a bandaged head and right arm.

He said the cadet, Vyacheslav Zolochevsky, "came to his senses near the wreckage of the An-26."

"The plane was destroyed, there was fire, darkness and bodies all around. One of the guys was burning," he said on Facebook, adding that Mr Zolochevsky rushed to try and save him. 

The Ukrainian president praised the cadet for his "heroism." "Ukraine is proud of you!" he said.

Doctors said Mr Zolochevsky suffered a concussion but his life was not in danger.

A tribute to the air crash victims at the National Air Force University in Kharkiv, Ukraine

Most cadets onboard were believed to be between the ages of 19 and 22.

President Zelensky said the cause of the crash should be quickly established and called for an "objective" investigation.

Investigators were looking at several possible causes of the crash including technical malfunction, human error and poor aircraft maintenance.

Rescuers inspect the crash site of the An-26 plane near Chuguev airport in Kharkiv, Ukraine

Defence Minister Andriy Taran said the plane "likely caught the ground with its wing" and then burst into flames.

Citing preliminary information, he said that one of the sensors in the left engine had failed. The final conclusion would be made after authorities analyse the plane's black boxes.