Forty-seven people remained unaccounted for.
Monday's accident occurred as the Lockheed Martin-built Hercules C-130 was taking off from Puerto Leguizamo on the border with Peru as it transported troops, Defence Minister Pedro Sanchez said on X.
The plane hit the ground just one-and-a-half kilometres away from where it took off, and ammunition being carried on board detonated as a result of fire on the aircraft, he later said.
There was no indication of an "attack by illegal actors," and the plane was airworthy with a qualified crew ahead of departure, Sanchez added.
Footage from the scene published by local outlet BluRadio showed thick plumes of smoke rising from the wreckage. One video showed the plane heading towards the ground just seconds after takeoff.
Two military sources earlier told Reuters that 71 people had been rescued from the wreckage.
Colombian Air Force Commander Fernando Silva said in a video posted on social media that the plane was carrying 114 passengers and 11 crew members, and that authorities were still investigating the cause of the crash.
In an earlier post on X, Petro criticised bureaucratic obstacles for delaying his plans to modernise the military.
"I will grant no further delays; it is the lives of our young people that are at stake," he said. "If civilian or military administrative officials are not up to this challenge, they must be removed."
Several candidates in Colombia's upcoming May 31 presidential election offered condolences and called for an investigation.
A spokesperson for US defence company Lockheed Martin said the company extended condolences to those affected by the crash and that it was committed to helping Colombia as it investigates the incident.
Hercules C-130 planes were first launched in the 1950s and Colombia acquired its first models in the late 1960s. It has more recently modernised some older C-130s with newer models sent from the US under a provision that allows for the transfer of used or surplus military equipment.
Hercules C-130s are frequently used in Colombia to transport troops as part of the military's operations amid a six-decade-long internal conflict that has claimed more than 450,000 lives.
The tail number of the plane that crashed on Monday matches that of the first of three US Air Force planes delivered by the US in recent years, which arrived in late 2020.
