Ukrainian President Volodymyr Zelensky on Saturday 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.

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

"Ukraine has lost 26 worthy sons," Zelensky 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, declaring Saturday a day of mourning.

The plane burst into flames on landing around 2 kilometres from the Chuguiv Military Air Base. 

On Saturday, the death toll rose after three more bodies were found under the charred remains of the plane and one of the two survivors died in hospital from extensive burns.

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 Zolochevsky rushed to try and save him. 

The second cadet died in hospital, the Ukrainian president said as he praised Zolochevsky for his "heroism".

"Ukraine is proud of you!" he said.

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

Most cadets onboard were believed to be between the ages of 19 and 22. Zelensky said the cause of the crash should be quickly established and called for an "objective" investigation.

Training flight 

Ukraine's SBU security service said the plane was performing a training flight but the cadets were not involved in piloting it.

The security service, citing preliminary information, said the pilot reported an engine failure and seven minutes later the plane hit the ground.

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

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

"Everything went according to plan: The plane was performing a training flight for cadets," he was quoted as saying by the defence ministry.

He said the instructor was at the wheel and cadets took turns to sit next to the pilot.

Taran said the aircraft was made in 1977 but could be operated for three more years without undergoing repairs.

On Friday, the plane made six take-offs and five landings, he said.

Several foreign leaders including Polish President Andrzej Duda, Canadian Prime Minister Justin Trudeau and the EU's top diplomat Josep Borrell expressed their condolences.

"We send our heartfelt condolences to the families and loved ones of the cadets, officers, and crew killed and injured in the An-26 plane crash," the US embassy in Ukraine said on Facebook.

The town of Chuguiv, with a population of more than 30,000 people, is located around 30 kilometres southeast of Kharkiv. 

Chuguiv also lies some 100 kilometres west of the front line where government forces are fighting pro-Russian separatists.

About 24 metres long and with a wingspan of 29 metres, the Antonov An-26 was designed in Soviet-era Ukraine.

Several military planes crashed during training flights in Ukraine in recent years.