Colombia's new President Juan Manuel Santos and Venezuelan President Hugo Chavez are to meet in Colombia for talks on Tuesday.
The two leaders are to discuss their countries' diplomatic rift, Colombia's foreign ministry said.
After Mr Santos' inauguration on Saturday, Mr Chavez said he would like to meet him "face-to-face".
Earlier, Mr Chavez urged Colombia's largest left-wing rebel group, Farc, to free all its hostages.
Mr Chavez has in the past successfully brokered a deal with the Farc rebels to release some of their hostages.
Last week, Farc said it was willing to search for a political solution to the 46-year-old conflict.
And Juan Manuel Santos began his presidency by signalling he would be willing to talk to the rebels if they freed their hostages.
The rebels have been a bone of contention between Venezuela and Colombia for years.
The issue flared up again last month, under Colombia's previous President, Alvaro Uribe, when the country called an extraordinary session of the Organisation of American States to formally complain about the alleged presence of Colombian rebels on Venezuelan territory.
The Colombian ambassador presented videos, photos and maps, which he said proved that there were about 1,500 rebels living and training in camps in Venezuela.
Hugo Chavez immediately denied the accusations and severed diplomatic relations with Colombia.
Relations appear to have softened since, with President Chavez sending his Foreign Minister Nicolas Maduro to the inauguration of President Santos on Saturday.
Mr Maduro and his Colombian counterpart, Maria Angela Holguin, held talks in Bogota on Sunday, to pave the way for the meeting between President Chavez and President Santos.
But while relations between the two neighbours may be about to improve, Mr Chavez signalled no rapprochement with the US was in sight.
On Sunday he rejected US President Barack Obama's appointment for ambassador to Venezuela.
He said he would not accept Larry Palmer as envoy because he had suggested morale was low in the Venezuelan army and raised concerns about Farc rebels finding refuge in Venezuela.
Mr Obama's national security adviser, General Jim Jones, was at President Santos' inauguration carrying "a clear message that the United States will continue its close bilateral ties and strong partnership with Colombia", the White House said.
"The general expressed our support for President Santos' interest in improving Colombia's relations with its neighbours through direct dialogue based on mutual respect," a statement from Washington said.
Speaking on his television show, Alo Presidente, Mr Chavez said the Farc guerrillas "should come out in favour of peace".
"They have no future by staying armed," he added, and told them to stop their campaign of kidnapping.
His message echoed that of Mr Santos, who in his inaugural address on Saturday said the door to dialogue with the Marxist group was open, but only if they freed their hostages first.
Colombia's military says rebel groups were still holding 79 people as of February 2010 but some non-governmental groups have put the number of those in captivity much higher.
Last week, Farc released a video message saying that it was willing to search for a political solution.
But Farc leader Alfonso Cano made no mention of the hostages.
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