Colombian President Alvaro Uribe has offered to create a temporary safe haven for peace talks, if left-wing guerrillas free hundreds of hostages.
President Uribe met hostage release advocate Gustavo Moncayo
Mr Uribe said he would then also be willing to release rebel prisoners.
He made the offer after meeting a man who walked across Colombia in protest at the plight of the hostages, among them his own son held since 1997.
The Farc has not responded officially but a website which carries rebel statements rejected the proposal.
"There will definitively be no humanitarian exchange with Uribe," a statement on the Anncol website began.
The president met Mr Moncayo, who was still wearing the chains he wore on his journey, at the protest camp he has set up in Bogota's historic Plaza Bolivar.
The schoolteacher from a remote town by the Ecuadorean border has taken Colombia by storm, says the BBC's Jeremy McDermott in Medellin. The man's soldier son, Pablo Emilio, was captured by Farc rebels 10 years ago when he was just 19.
After speaking to Mr Moncayo, Mr Uribe addressed a noisy crowd of several thousand people who had gathered in the square.
He repeated his rejection of a Farc demand for a demilitarised zone in south-west Colombia to allow peace negotiations to take place.
"The only reason for a demilitarised zone is for the criminals to hide from the security forces," he said.
"I won't hand over one millimetre to the criminals."
Mr Uribe did say, however, that he would be willing to create a special zone in order to begin peace talks and release Farc prisoners - once the rebels released their hostages.
"If the Farc frees kidnap victims with the help of the international community, the government will accept a zone for talks for 90 days on reaching peace," Mr Uribe said.
Scores of politicians, police and soldiers have been kidnapped and are held in secret jungle lairs by the rebels.
Analysts say Mr Uribe's proposal is unlikely to persuade the Farc to free key hostages they can use for political leverage.
Mr Moncayo has vowed to camp out in the square until the government and the rebels agree to swap prisoners, calling on both sides to end what the termed their "political game".
"Sadly our children, our loved ones are still in the jungle, Despite all the things that have been done, they remain kidnapped and we are here caught in the middle of this game," he said.
"It hurts me because we have been the ball, caught in the middle of a game where they have taken as much advantage as possible."