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.
Defence Minister Pedro Sanchez said earlier on X the accident happened as the Lockheed Martin-built Hercules C-130 was taking off from Puerto Leguizamo on the border with Peru, as it transported troops.
"The exact number of victims and the causes of the crash have not yet been determined," he said.
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 take-off.
BluRadio said the crash took place just 3km from an urban centre.
Two military sources told Reuters 71 people had been rescued from the wreckage.
Silva put the figure at 48 in the earlier video message.
"I hope there are no fatalities in this horrific accident that should never have happened," President Gustavo Petro said in a post on X, in which he 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."
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 law that allows for the transfer of used or surplus military equipment.
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