Colombia's government says it has made a new offer to the main left-wing rebel group, the Farc, to hold talks about a prisoner exchange.
The Farc want to see their fighters freed from jail
The government said it could hold talks with the Revolutionary Armed Forces of Colombia in a southern district.
It promised the army would not carry out any military operations in the Pradera municipality at the time.
The rebels are believed to be holding 60 hostages who could be exchanged for imprisoned rebels.
Former presidential candidate Ingrid Betancourt and three US defence contractors are among those being held by the Farc.
In the past, the Farc has demanded the demilitarisation of two complete municipalities before discussions could start.
Correspondents say it is unlikely the guerrillas will accept the new government terms.
The offer from the government of President Alvaro Uribe follows moves earlier this week to begin peace talks with Colombia's second rebel group, the National Liberation Army.
A peace process with the country's main right-wing paramilitary group, the AUC, is already under way - but the terms of it have been strongly criticised by human rights groups.
Colombia's long-running civil conflict has pitted left-wing guerrillas against right-wing paramilitaries and state forces.
Tens of thousands of civilians are known to have died in the 40-year conflict.