Colombia is prepared to pull out troops from a small mountainous area to hold talks about exchanging hostages for jailed rebels, the government has said.
Colombian-French national Ingrid Betancourt was kidnapped in 2002
In what is seen as a U-turn, President Alvaro Uribe said he accepted proposals by an international commission to break a deadlock with the left-wing Farc.
The rebels are holding some 60 hostages - including foreigners - several of whom were seized several years ago.
There was no immediate response from the Farc to Mr Uribe's statement.
The rebels want to exchange hostages for jailed guerrillas.
Among the kidnapped people are three US nationals and a former Colombian presidential candidate, who has dual Colombian-French nationality.
However, it is far from clear whether the talks will go ahead, as the rebels have been insisting on other pre-conditions as well, correspondents say.
Demilitarisation of 180 sq km (69.5 sq miles) in south-western Colombia
Talks to take place in the small town of El Retiro
40 international observers to attend
ICRC to be in charge of negotiators' safety
The Farc, or Revolutionary Armed Forces of Colombia, and the smaller National Liberation Army (ELN) have been involved in a 40-year conflict with state forces and right-wing paramilitary groups.
The government is currently holding preliminary peace talks with the ELN in Cuba.
It also has started a peace process with the country's main paramilitary group, the United Self Defence Forces of Colombia (AUC).
But the Farc has so far refused to negotiate with President Uribe.
The Colombian government says the 180 sq km (69.5 sq miles) to be demilitarised is in the area around Pradera, some 270km (170 miles) south-west of the capital, Bogota.
The rural region in the Valle del Cauca department includes the small town of El Retiro, home to 30 families, where President Uribe wants the talks to take place.
The zone is considerably smaller than what the rebels have been demanding in order for negotiations to proceed.
Mr Uribe said the international commission - made up of officials from France, Spain and Switzerland - suggested a temporary troop withdrawal in the area in a proposal sent to both the government and the Farc.
"We accept it because we want to understand the anguish, the pain, the suffering of so many Colombians who have family members who have been kidnapped," Mr Uribe said at a news conference.
"I confess this is a concession on the part of my government," he added.
Under the Colombian authorities' plan, 40 international observers will oversee the talks and the International Committee of the Red Cross (ICRC) will be in charge of the negotiators' safety.
The BBC correspondent in Colombia, Jeremy McDermott, says that despite the radical shift in the government's position, it is unlikely that the Farc will agree to the proposal.
The rebels have repeatedly said that Mr Uribe is not serious about negotiations but simply is trying to strengthen his position for next year's presidential elections, he adds.