The UN secretary general has said the peace talks in Colombia between the government and paramilitaries should result in the fighters' disarmament.
Some 400 fighters gathered in the "safe zone" in the north
In a statement issued in New York, Kofi Annan also warned that the process should not permit general amnesties or immunity from prosecution.
The talks began on Thursday inside an area in which the right-wing AUC are immune from arrest or extradition.
However, observers are not optimistic about prospects for the negotiations.
Some Colombian newspapers hailed the talks as "unprecedented" in scale, but many commentators are gloomy about the prospects of the paramilitaries laying down their arms.
About 10 leaders of the AUC (United Self-Defence Forces of Colombia) and some 400 fighters providing what they said was security entered the safe zone, which covers about 360 sq km (147 sq miles).
Among those at the talks in the town of Santa Fe de Ralito in Cordoba province are fighters suspected of some of the country's worst human rights abuses.
The AUC have presented five proposals aimed at bringing about a permanent ceasefire, according to local media reports.
These include the creation of new safe areas for fighters and guarantees for their re-integration into civilian life.
Government officials including peace commissioner Luis Carlos Restrepo are also attending the talks.
They want to see the AUC demobilised by 2006.
The talks face a number of seemingly insurmountable obstacles, says the BBC's Jeremy McDermott in Medellin.
Key among them is that many of the paramilitary leaders are alleged to be Colombia's biggest drug traffickers - at least five have US extradition warrants pending.
The paramilitaries have said they refuse to spend a single day in prison or face extradition - while Washington has made it clear that the subject of extradition is not negotiable.
Human rights groups are also keen that the paramilitaries be held fully to account for some of the abuses they are alleged to have committed.
The AUC is accused of massacres and selected killings of trade unionists and left-wing rebels, among other abuses.
The talks began less than a day after the release of former senator Jose Gnecco - whose kidnap on Sunday along with his family nearly wrecked the negotiations.
"I want to thank God for returning alive. I want to thank the president, the government, the peace commissioner, the military and all those who contributed to my release," a sobbing Mr Gnecco told reporters after he was set free.
The abduction incensed the government, who quickly accused two top AUC leaders of involvement, stripping them of immunity from arrest.
Rodrigo Tovar Pupo - alias Jorge 40 - and Hernan Giraldo have now had their immunity restored and the government has said they are free to join the talks.
But reports suggest Mr Tovar has accepted responsibility for the kidnapping and has voluntarily removed himself from the talks.