Ms Betancourt said she wants all of Farc's hostages released
Freed Colombian hostage Ingrid Betancourt has urged that leftist Farc guerrillas release all their captives and engage in a peace process.
The French-Colombian politician was rescued on Wednesday after being held for more than six years by Farc rebels in the jungles of Colombia.
She has been reunited with her family and is flying to France.
She is to be met by President Nicolas Sarkozy before attending a lavish public welcome in Paris.
Mr Sarkozy campaigned for her release, and sent a medical team to Colombia in an unsuccessful attempt to get her medical treatment.
Ms Betancourt was among 15 hostages rescued without a shot being fired as their rebel captors were tricked into handing them over.
At a press conference in Bogota, she said that Farc had the opportunity to hand over their remaining hostages and take the path towards peace.
"I hope that the Farc understands that this is the time to release all its hostages and use this release, this act, not only to improve its now tarnished image, but especially for us here in Colombia, to try to make this the first step towards a negotiated peace."
The Revolutionary Armed Forces of Colombia, or Farc, has been waging a war against the state for the past four decades. They still hold more than 40 high-profile hostages, and several hundred other captives.
She said she wanted: "A speedy peace process, a peace process without impunity, without conditions favourable to one side, a process that allows for an impetus to change to the structure of the Colombian state for the good of all Colombians."
Ms Betancourt was campaigning for the presidency against current incumbent Alvaro Uribe when she was kidnapped in a Farc-controlled area of southern Colombia in 2002.
After her release she thanked Mr Uribe and said she still aspired "to serve Colombia as president".
Mr Uribe was first elected president in 2002. He has pursued a hard-line stance against Colombia's left-wing guerrillas while making tentative peace overtures.
Ms Betancourt said she would work tirelessly for the freedom of all hostages being held by Farc rebels but said the group was "finished".
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The moment Ingrid Betancourt was reunited with her children
"What happened yesterday was a dramatic blow to the structure of the organisation.
"Firstly in the sense that they were infiltrated, secondly there was a breakdown in communications with leaders, a lack of co-ordination in their operations, a lack of logistics, in short it is an organisation that is finished," she said.
A disgruntled Farc member who had gone over to the government side had infiltrated the group's leadership and convinced them to move Betancourt and 14 other hostages to a rendezvous point in the jungle.
Waiting there were Colombian soldiers, posing as members of a non-government organisation.
CAPTIVITY TIMELINE
Feb, 2002: Betancourt kidnapped by Farc rebels
Feb, 2003: US defence contractors Thomas Howes, Keith Stansell and Marc Gonsalves seized by after their plane goes down in southern Colombia
Jan, 2008: Betancourt aide Clara Rojas and ex-congresswoman Consuelo Gonzalez freed by Farc
March, 2008: Colombian forces raid rebel camp in Ecuador and kill Farc commander Raul Reyes
March, 2008: Farc leader Manuel Marulanda dies of reported heart attack
July, 2008: Colombian military frees Ms Betancourt, the three US contractors and 11 other hostages
They freed Ms Betancourt, three Americans and 11 members of the Colombian security forces and flew them to freedom.
The freed Americans - military contractors Marc Gonsalves, Thomas Howes and Keith Stansell - were flown to Texas late on Wednesday, and the US military later said they all were "in a very good physical health".
The local commander in charge of the hostages, a man known as Cesar, and another rebel were captured in the operation and will face justice, the authorities say.
Ms Betancourt later had a tearful reunion with her two children, Melanie and Lorenzo Delloye-Betancourt, who had flown to Bogota from France.
They were 16 and 13 when she was seized.
She described the reunion as "an orgy of kisses".
The operation was carried out with the help of US spy satellites which tracked the rebels and the hostages on a weeks-long journey through the jungle that ended with the rescue.
The BBC's Jeremy McDermott, in Medellin, says the successful operation by Colombian security forces is a political and military coup for the country's government and a major blow to the Farc.
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