Dominican President Leonel Fernandez opened the 20-nation Rio Group summit with a call for unity.
"What is least helpful in these moments in our Latin America ... is to act in a disunited way," Fernandez said. Uribe and Chavez, separated by two seats, listened intently.
The summit was to have focused on energy and other issues, but the diplomatic crisis in the Andes now has center stage. It was triggered by a deadly Colombian cross-border raid into Ecuador on Saturday that killed a senior Colombian rebel.
"People should go cool off a bit, chill out their nerves," Chavez told journalists at his hotel before leaving for the summit at the foreign ministry of the Dominican Republic. "I think the meeting today is going to be positive, because it is going to help the debate. We have to debate, talk, and this is the first step toward finding the road."
Chavez has ordered thousands of troops and tanks to Venezuela's border with Colombia and threatened to slash trade and nationalize Colombian-owned businesses. Ecuadorean President Rafael Correa has also sent troops to the border, although Colombian President Alvaro Uribe has said he won't do the same.
The summit marks the first face-to-face encounters between Chavez, Correa and Uribe since the international crisis began.
Correa told reporters he wants Uribe to apologize for the attack in Ecuadorean territory and give his "formal and firm commitment" that Colombia will never "violate" the sovereignty of another country.
On his arrival in Santo Domingo late Thursday, Chavez took shots at Colombia and the United States, which has supported the Andean nation with more than $4 billion in counterinsurgency and anti-drug aid since 2000.
"The U.S. empire has taken over Colombia," Chavez said.
Chavez claimed the strike that killed Raul Reyes, a top leader of the Revolutionary Armed Forces of Colombia, or FARC, was "planned and directed by the United States." Later, he said he had information that "gringo soldiers" participated in the attack, but provided no evidence.
U.S. Southern Command spokesman Jose Ruiz neither confirmed or denied this week that the U.S. military took part in the attack that killed Reyes and 23 others.
Uribe is hugely popular among Colombians for cracking down on the FARC, which finances itself through kidnapping and drug trafficking. He declined to comment on the crisis as he arrived in the Dominican Republic.
Uribe has defended the attack as necessary given Ecuador's inaction against Colombian rebel camps in its territory. Colombia complains that rebels take refuge across the border in Ecuador and Venezuela and has accused their leftist leaders of backing the fighters - a claim the leaders deny.
Uribe has refused to rule out future military incursions into Ecuador or Venezuela, saying he first needs assurances from Correa and Chavez that they are not harboring rebels.
The crisis widened Thursday when Nicaragua broke off relations with Colombia. Nicaraguan President Daniel Ortega, who is also attending the summit, is an ally of Chavez and Correa.
Latin American foreign ministers on Thursday drafted a statement saying national sovereignty must be respected. The draft, to be submitted to the presidents on Friday, mirrors one earlier in the week from the Organization of American States, said Chilean Foreign Minister Alejandro Foxley.
One of the rare regional voices offering support for Colombia was Salvadoran President Tony Saca, who said the Colombian government should be able to defend its citizens.
"We need to understand Colombia has the legitimate right to go after terrorists ... wherever they may be, of course without harming the sovereignty of another country," Saca said on arrival in Santo Domingo.
Colombia's defense minister said Friday that another FARC leader had been killed by one of his own guerrillas.
"The FARC has suffered a new, major blow," Defense Minister Juan Manuel Santos said at a news conference, calling Rios' death "yet another demonstration that the FARC are falling apart."
Santos said troops launched an operation designed to capture Rios on Feb. 17 after receiving tips that he was in a mountainous area straddling the western provinces of Caldas and Antioquia, and engaged the guerrillas' outer security ring seven times.
Thursday night, he said, a guerrilla known as Rojas came to the troops with Rios' severed right hand, laptop computer and ID, saying he had killed his boss three days earlier.
It was unclear what motivated Rojas to kill his boss, but Santos said it was to "relieve the military pressure" because the rebels were "surrounded, without supplies and without communication."
The U.S. State Department has a standing bounty of $5 million for Rios' capture.
In Ecuador, Security Minister Gustavo Larrea said the army captured five suspected FARC rebels on Thursday. The suspects were nabbed "a few meters from the Colombian border," in the general area where the raid took place, Larrea said.