Colombia's turnaround came two days after Fernando Araujo, the foreign minister, blamed December's failed mission on "people unfamiliar with Colombia's conflict" saying it "left a bad taste".
Al Jazeera's Monica Villamizar, reporting from Bogota, said the foreign minister had misunderstood the real position of the government, which is to welcome international help as long as mediation efforts are done discreetly.
Chavez had gathered five leftist Latin American leaders and US film-maker Oliver Stone to witness the hostage pickup in December, only for the rebels to make a U-turn at the last minute.
Colombian politicians Consuelo Gonzalez and Clara Rojas, along with Rojas's young son, Emmanuel, were supposed to have been released on New Year's Eve but Farc leaders aborted the mission citing army operations within the area.
The fiasco deepened the diplomatic spat between Chavez and Alvaro Uribe, the Colombian president, which had first errupted after Uribe tried to exclude Chavez from earlier hostage talks, accusing him of blocking the release plan.
It later emerged the child was actually living with a foster family in Bogota.