Juan Manuel Santos said that Seusis Hernandez could be extradited to the United States after his arrest on drug trafficking charges.
Jesus Santrich, a former peace negotiator, is accused of drug trafficking by a court in NY.
FARC has also requested observation of the United Nation, the European Union and the worldwide community to ensure the Colombian state fulfills their part of the 2016 Havana peace agreement.
FARC ex-guerrilla member Ivan Marquez, who now also holds a leadership spot in the political movement, confirmed the arrest and condemned it. Marquez said the arrest marked the "worst moment" that the peace agreement was going through.
Colombian authorities arrested ex-FARC guerrilla leader Seuxis Hernandez Solarte, known by his alias "Jesus Santrich", on Monday in Bogota, after he was indicted for drug trafficking by a court in the United States.
"If due process is fulfilled - and if there is irrefutable evidence - then there are grounds for extradition for crimes committed since the signing of the (peace) accord, and I will not stay my hand in authorising that", Mr Santos said.
In its last sentences, the press release expresses FARC's solidarity with Jesus Santrich and support to the hunger strike he has started.
"Those detained have betrayed the values and the principles of the peace deal", Martinez said. The statement also condemned the "subordination of Colombia's justice system" to USA interests. The FARC, speaking before Trump cancelled the trip, said Santrich shouldn't be handed over as a "trophy" to Trump. Mr Santrich will remain in custody until the U.S. requests his extradition.
Under the agreement, FARC fighters who demobilise and confess to war crimes would be spared jail time and extradition, but this protection does not extend to crimes committed after the peace deal was ratified.
A special tribunal set up by the accord will rule on whether Santrich's alleged past crimes are covered by the agreement in what experts say is a major test for the peace process' credibility.
Waving white flags emblazoned with the red rose symbol of the former rebels" political movement, some shouted "freedom' and denounced what they called an act of judicial sabotage by the government and its USA backers.
But the rebels always denied direct involvement in the business itself and rebel peace negotiators in 2013 denounced drug trafficking as a "scourge" that has "contaminated" the worldwide financial system and generated a global health crisis.
'The senior leadership never cut ties to the cocaine production that earned them billions of dollars as an insurgence, ' said Douglas Farrah, a senior visiting fellow at the National Defense University who has testified to the U.S. Congress on the FARC's criminal ties.