Colombia and Venezuela have welcomed an offer by Brazil to mediate in their dispute over the kidnap and arrest of a Colombian guerrilla commander.
Colombia paid mercenaries to capture Granda
Colombian President Alvaro Uribe said both countries had an interest in maintaining positive ties.
He was speaking before a summit with Brazil's president at which the offer was expected to be discussed.
Earlier, Venezuela's foreign minister said he was confident his government could improve relations with Colombia.
Ties between the two countries have deteriorated in a dispute over whether Colombia had the right to pay for the capture of a Colombian guerrilla commander, Rodrigo Granda, in Venezuelan territory.
Venezuela has withdrawn its ambassador in Bogota and cut some commercial links, but minister Ali Rodriguez said diplomatic ties would not be broken off.
Peru has also offered its good offices, while Mexico is proposing that the Organisation of American States also become involved.
Venezuela has rejected Colombia's suggestion of a regional summit to resolve the dispute.
However, President Hugo Chavez said he was ready to talk face-to-face with his Colombian counterpart Alvaro Uribe.
Before the dispute, relations had been warming
But he said Colombia would first have to apologise for what he is calling a crime against Venezuelan sovereignty.
Before his assembled cabinet and with millions of Venezuelans watching on TV, President Hugo Chavez stretched out his hand to the camera and spoke directly to the man he called his friend.
"I do not believe you knew what was going on," he told Alvaro Uribe, but he said the Colombian president must now recognise the crime against Venezuela's sovereignty committed by his officials.
He also made clear he believed the conflict had been engineered by those in both countries and in the United States who want to undermine good relations between the two countries.
The US on Saturday offered its "100% support" for Colombia's actions.