"By common consent, it was decided to postpone the start of this round of talks, because they asked for more time to work on the issue of illegal drugs," the source said yesterday.
"I do not yet have a precise date" for when the talks will resume in Cuba, he added.
The postponement comes two days before the process was set to mark the one-year anniversary since the talks began on November 19, 2012.
The two sides must also still resolve questions on compensation for victims and disarmament.
The half-century old guerrilla war -- Latin America's longest-running insurgency -- has left hundreds of thousands of dead and displaced more than 4.5 million people.
The Revolutionary Armed Forces of Colombia, or the FARC, has some 7,000 to 8,000 fighters, Colombia's largest rebel group.