"I have ordered the creation of a special unit for the persecution of these criminals with reinforced intelligence, investigation and mobility capabilities throughout Colombian territory," Duque said.
The ex-FARC leaders were being backed by Venezuela's socialist President Nicolas Maduro, Duque said.
"Colombians must be clear that we are not facing a new guerrilla, but facing the criminal threats of a gang of narco-terrorists who have the shelter and support of the dictatorship of Nicolas Maduro," the Colombian president said.
Duque was responding to a declaration by former guerrilla leader Ivan Marquez that he and other former rebels would resume fighting.
Marquez made the announcement in a video in which he appears in the Colombian jungle flanked by 17 men and women holding rifles. Behind them is a yellow FARC banner.
Duque was elected last year on promises to modify the 2016 peace accord with the FARC on the grounds that it was too lenient to ex-fighters guilty of serious crimes.
He announced a reward of three billion pesos (around $882,000) for the arrest of each of the men and women who appear in the video.
"Let's not fall into the trap of those who today are trying to hide behind false ideological clothing to sustain their criminal scaffolding," he said.
Although most of the 7,000 FARC fighters laid down weapons to return to civilian life, around 2,300 distributed in different groups have refused to do so.