The leaders of the three countries sat down with other presidents at the Rio Group summit in Santo Domingo in their first encounter since their dispute erupted when Colombia struck a FARC rebel camp inside Ecuador last weekend.
The attack prompted Venezuela and Ecuador to deploy extra troops to their borders, and break off relations with Colombia.
"The region is experiencing a rare moment of very grave consequences if we do not act in time," Ecuadoran President Rafael Correa warned his counterparts at the meeting in the Dominican Republic's foreign ministry.
Correa has urged the Rio Group to "clearly condemn" Colombia for the strike, which left 23 rebels dead including FARC number two leader Raul Reyes.
Uribe admitted that he had not warned Correa in advance about the strike, but he charged that the Ecuadoran leader's lack of cooperation against the FARC forced Colombia to keep the operation secret.
"We have not gotten cooperation from President Correa in the fight against terrorism," he said.
Chavez, speaking to reporters before the summit, said "minds and nerves must cool down" in order to end a conflict that risks "internationalizing."
The summit of 20 Latin American democracies had been scheduled before the dispute, but regional leaders fully expect to discuss the crisis and hope the three presidents will meet face to face.
Chilean President Michelle Bachelet, who attended the summit, said earlier that the gathering should serve as a "space for dialogue and compromise."
The Rio Group was created in 1986 to expand political cooperation between Latin American nations, and to help find solutions to problems in the region.
The crisis widened Thursday when Nicaragua joined Ecuador and Venezuela in breaking diplomatic relations with Colombia over the strike, which killed 23 FARC members including a commander.
Nicaragua's leftist president, Daniel Ortega, urged the Rio Group to issue "a condemnation against terrorist acts such as the one committed by Colombia against Ecuador."
After Saturday's attack, Venezuela ordered 10 battalions, counting at least 6,000 men, to the border with Colombia, along with tanks and armored vehicles. Ecuador has also deployed troops to its Colombian frontier.
Colombia has ruled out sending reinforcements to its borders.
The Revolutionary Armed Forces of Colombia (FARC), a Marxist rebel group fighting the Colombian government for four decades, have been reported to hide in Venezuela and Ecuador.
The Washington-based Organization of American States approved a resultion Wednesday saying Colombia had violated Ecuador's sovereignty, but it resolution stopped short of formally condemning Bogota.
The United States has backed Colombia, its staunchest ally in Latin America, since the crisis began and criticized Venezuela's involvement in the dispute.
Colombia has received billions of dollars in US military aid in its fight against drug trafficking and the Marxist rebels.
For his part, Chavez has been a thorn in Washington's side for years, while his relations with Uribe began to deteriorate late last year.
Uribe has accused Chavez of providing support to the FARC, while the Venezuelan leader dismissed the Colombian president as a US lap dog.
Correa has also charged that Saturday's attack thwarted the potential release of 12 hostages, including French-Colombian politician Ingrid Betancourt, being held by the FARC.
The FARC, which are accused of drug trafficking and holding more than 700 hostages, are on US and European Union lists of terrorist groups.