But the rescue-operation hopes evaporated on Monday.
Both Farc and Chavez accused Alvaro Uribe, the Colombian president, of wrecking the plan by ordering military operations in the jungle region where the three captives were believed to be held.
Uribe denied the allegation and accused Farc of lying.
Uribe said his government had given Venezuela and the International Red Cross co-ordinating the mission every guarantee that its military would not obstruct the handover.
That included a promise to create a ceasefire corridor to allow Farc members to escort their hostages through the jungles to the pickup point.
Uribe, whose father was killed in a botched Farc kidnapping over 20 years ago, is popular for cutting violence and crime with his crackdown on the fighters.
|The deal to free the hostages had been brokered by Chavez [Reuters]|
But Farc still controls wide rural areas used to produce the cocaine that funds its armed anti-government campaign.
The three hostages are Consuelo Gonzalez, Clara Rojas and her son Emmanuel, who was fathered by a Farc fighter and is thought to be about four years old.
Rojas was kidnapped during Betancourt's vice-presidential campaign and Gonzalez, a former legislator, was taken in 2001.
Meanwhile, relatives of Emmanuel are to undergo DNA testing to determine whether the child is still a captive or is in a Bogota orphanage, as Uribe has charged.
Uribe caused a stir by saying that Emmanuel was actually in Bogota at a state-run orphanage of the Colombian Family Welfare Institute (ICBF), and had been there since July 2006.
He urged DNA tests on Emmanuel's grandmother to determine the truth.