The former Colombian presidential candidate is reported to be seriously ill
The French humanitarian mission sent to Colombia to try to secure to release of the hostage Ingrid Betancourt is being withdrawn from the country.
Colombia's Farc rebels said they would not allow emergency medical aid to be delivered to the kidnapped politician.
The mission was "not acceptable" and was launched without the guerrillas' agreement, a Farc statement said.
France, Spain and Switzerland, which were jointly behind the mission, said it was "no longer justifiable".
"It will therefore leave Colombia soon," the three countries said in a statement.
French Foreign Minister Bernard Kouchner will travel to the region "soon" to discuss the situation, an official statement said.
President Nicolas Sarkozy had announced the French mission after reports that Ms Betancourt, who holds dual French-Colombian citizenship, was seriously ill.
She was kidnapped while campaigning for the Colombian presidency six years ago.
"The French medical mission is not acceptable and much less so when it is not the result of a prior agreement," said a rebel statement, which was issued online by Farc's ruling secretariat.
"We do not act under blackmail or under pressure from media campaigns," it added.
The statement called on Colombia's government to establish a demilitarised zone where hostages could be swapped for jailed rebels.
The French mission has been grounded outside Bogota since Thursday
Farc wants to exchange 39 high-profile hostages for some 500 rebels currently in prison.
Colombian President Alvaro Uribe has consistently rejected the request.
However, his government has promised to suspend military operations against Farc in the area where many of its hostages are believed to be held.
Ms Betancourt was pictured looking thin and frail in a recent video.
France also offered to take in rebels released from prison in exchange for the 46-year-old, who has been held in the jungle since 2002.
Farc - the Revolutionary Armed Forces of Colombia - has been fighting the Colombian government for more than 40 years.