Colombia's left-wing guerrillas, the Revolutionary Armed Forces of Colombia (Farc), have said they are prepared to negotiate with the government.
The Farc and ELN have been at war with the state for decades
Farc would talk to President Alvaro Uribe if he ended US-backed operations against them and demilitarised swathes of jungle territory, a spokesman said.
The group is also prepared to exchange some 60 hostages, the spokesman told Venezuelan TV channel TeleSur.
Mr Uribe has stressed he will not agree to the guerrillas' terms.
In recent months Farc has rejected any suggestions of formal negotiations.
Mr Uribe, who recently won re-election to the presidency, has repeatedly said he will not halt operations against rebels and narco-traffickers, or withdraw security forces from rebel-dominated territory.
A government spokesman told the Reuters news agency that position had not changed.
Colombia's other main armed group, the ELN, is currently holding preliminary peace talks with Mr Uribe's government.
Farc spokesman Raul Reyes told TeleSur the organisation had "all the political will" to allow an exchange of hostages.
Hostage-taking has played a key role in Colombia's conflict for many years.
Former presidential candidate Ingrid Betancourt is thought to be among the hostages held by Farc, as are some 50 soldiers and police.
Three Americans and some politicians are also in captivity. Farc wants to exchange them for some 500 rebel soldiers.
But Mr Reyes added that the group would only come to the negotiating table on its terms.
"The Farc won't accept talks under the table, in private, outside the country or any place in Colombia with this government until these areas are demilitarised," he said.
"It is Alvaro Uribe who will decide whether to continue the war or seek to sit down with the Farc."