Regional governor Jhon Gabriel Molina said this in a video statement, according to AFP.
The transport plane, a C-130 Hercules, had 125 people on board when it crashed in a rural area of Puerto Leguizamo near the border with Ecuador, according to television company RCN, which showed images of black smoke billowing from the aircraft's fuselage.
Some of the survivors have serious injuries, the daily newspaper El Tiempo reported.
According to the Colombian military, there were 11 crew members and 114 soldiers on board.
The accident occurred in an area where drug trafficking is widespread and where militant groups opposed to the government in Bogotá are also active. In addition, drug-related crime has shifted across the porous border between Ecuador and Colombia.
According to information from the military, the country's forces had carried out an operation against one of the area's drug cartels.
The crash is the second involving a Hercules aircraft in South America within a month. 24 people died when a Bolivian military plane crashed while landing on February 27.
