Colombia recently said seven FARC leaders are operating in Venezuela and two are in Ecuador.
But officials estimate that some 8, 000 Farc guerrillas are still fighting Latin America's longest-running insurgency.
He, in turn, pressured Uribe to start a dialogue with the FARC to release her.
The government scored a major breakthrough with the November 2011 killing of FARC leader Alfonso Cano.
The United States has designated both the FARC and the ELN as foreign terrorist organizations.
FARC's fishing rules, asked whether the rebels were concerned with conserving the fish or the dynamite.
Clashes between the Farc and the ELN have been intensifying since the beginning of the year.
He said Mr Perez was the head of the Farc's international front in Europe.
The Farc's attempt to win similar support in Ecuador has been less successful, the IISS concludes.
His security build-up drove the FARC from heavily populated central Colombia to remoter areas.
FARC, led to a clash between Mr Samper and the then armed-forces commander, General Harold Bedoya.
The government negotiators have so far made no comments on the latest Farc move.
BBC: Ivan Marquez (left) and fellow Farc negotiator. File photo
The Farc, who numbered 16, 000 in 2001, are now thought to have some 8, 000 fighters.
BBC: Ivan Marquez (left) and fellow Farc negotiator. File photo
Earlier this year, the Farc said they would no longer resort to kidnapping or holding prisoners.
With a successful negotiation that includes FARC into politics, the situation will change radically.
It has been five years since Ingrid Betancourt, former Colombian Presidential Candidate was kidnapped by FARC.
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The Farc's chief negotiator, Ivan Marquez, has ruled out an extension of the 20 January ceasefire.
He also says he would never talk to the FARC unless they accept the constitution.
This would leave Colombia's Alvaro Uribe almost alone at the mercy of the FARC.
Ms Betancourt, a dual Colombian-French national, was seized by the FARC in February 2002.
Mr Santos had previously said that a precondition for proper peace talks was that the FARC declare a ceasefire.
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What has worried Colombian officials most has been signs that Venezuela has been helping the FARC.
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Colombia's Farc rebels have said their ceasefire will be suspended on 20 January, as initially planned.
There is even new support in the U.S. Congress for helping Colombia fight the FARC.
In fact a former senator and FARC-hostage, recently fled Colombia after he received several death threats.
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FARC's smaller cousin has for some time seemed almost desperate to give up its war.
The prospects for successful talks with the FARC look better than ever before.
ECONOMIST: This time negotiations might eventually bring peace
Mr. McGovern said in a letter to this newspaper that the FARC was engaging in fantasy.
Colombia has tried peace talks with the Farc before, says Jose Obdulio Gaviria, a former Uribe adviser.
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