"They will be free in a humanitarian way, that war is not the only way and that they are going to get out of there, that Colombia's going to know peace.
"Humanitarian [concerns] must come before the war" against the Farc.
Betancourt's children made the appeal during a vigil held for their mother outside Notre Dame cathedral in Paris, France.
Betancourt has been held hostage for five years by Farc.
|Melanie, left, and Lorenzo, second left, called|
for the release of their mother in Paris [AFP]
Farc is offering to free some high-value hostages - who include three US defence contractors taken nearly five years ago - in return for the release of hundreds of imprisoned members of their group. Hugo Chavez, the Venezuelan president, was trying to help negotiate a prisoners-for-hostages swap until Uribe called off the arrangement last month, saying Chavez had overstepped his mandate.
Chavez said: "There's little we can do because it depends on the willingness of the two sides and, in Colombia, especially on the part of the government, there is no willingness for a humanitarian exchange.
"They don't want that, even though they say they do, they don't."
Uribe called for the group to hand over the hostages to either Nicolas Sarkozy, the French president, or Chavez, and called for their unilateral and unconditional liberation.
Farc announced this week that it would release three hostages to Chavez.
Those likely to be released are Consuelo Gonzalez, a former congresswoman; Clara Rojas, an aide to Betancourt, who is a former Colombian presidential candidate; and Rojas' young son, reportedly born of a relationship between her and a guerrilla fighter.
"Suddenly, things are moving," Melanie Betancourt, Ingrid's daughter, said.
But she said that the need for action was more urgent now than ever.
"The day they [the three] are freed ... that day the world will not be able to deny that the Farc will have made a humanitarian gesture of goodwill.
Onus on Uribe
Melanie Betancourt said: "At that moment, I'm sorry, it will be necessary for the Colombian President Alvaro Uribe ... to recognise that the ball is in his court."
That means, Melanie said, "it is up to him to take the next step to finally make a humanitarian exchange".
Cardinal Andre Vingt-Trois, president of the Conference of Bishops in France, attended the vigil and urged church officials in Colombia to add their weight to the campaign, which has become an affair of state in France.
In a statement sent to his Colombian counterpart, Vingt-Trois said French bishops were praying "for the efforts of the Colombian church toward negotiations and a peaceful solution".
Sarkozy discussed the hostage drama with Pope Benedict XVI at the Vatican on Thursday, and has received Chavez at the presidential palace in Paris.