(Adds Castro comments)

By Patrick Markey and Enrique Andres Pretel

SANTO DOMINGO, March 7 (Reuters) - The presidents of Colombia, Ecuador and Venezuela ended a border dispute on Friday with a summit handshake after a week of regional diplomacy in the face of hostile rhetoric and troop buildups.

"And with this ... this incident that has caused so much damage (is) resolved," leftist Ecuadorean President Rafael Correa said before standing up and shaking hands with his U.S.-backed conservative Colombian counterpart, Alvaro Uribe.

Venezuelan President Hugo Chavez, who had blamed the United States for the crisis as he sent tanks to the border with Colombia, joined in shaking Uribe's hand and applauded loudly and smiled.

The dispute erupted last Saturday when Colombia raided inside Ecuador to kill a rebel leader. It resolution brought the summit to a surprise ending after bitter exchanges, including Correa calling Uribe a liar.

The accord came after Uribe apologized to Correa under pressure from governments across the region, which worked to prevent the crisis escalating into Latin America's first armed conflict among states in more than a decade.

The dispute had spread across the region with leftist allies Venezuela and Nicaragua joining Ecuador in cutting relations with Colombia, while Venezuela and Ecuador sent troops to their borders against the strongest U.S. ally in the region.

Uribe also moved to meet another Correa demand, guaranteeing Colombia would not make similar raids if his neighbors cooperated in the fight against the Revolutionary Armed Forces of Colombia, or FARC.

The resolution was a diplomatic victory for Latin America, whose governments from Mexico to Brazil managed the crisis by emphasizing negotiations and took advantage of their previously scheduled summit to force the sides to talk.

Still, the crisis exposed a left-right rift and sparked controversies that could dog the leaders even if their tough stances in the crisis generally bolstered their support at home.

Uribe, popular for a U.S.-financed military offensive against the guerrillas, had said Chavez and Correa supported "terrorists" and they dragged up old accusations he was friendly with paramilitary drug traffickers.

HANDS FOR PEACE

The summit host, Dominican Republic President Leonel Fernandez, engineered the handshakes, broadcast live on television across Latin America, by appealing to the leaders to make the public gesture.

"This summit was a gift from God," Chavez said. "We are all happy. Peace! ... we must unite and integrate."

Uribe, who for years had maintained a generally warm relationship with his ideological opposite, recalled that friendship before ending the dispute.

The regional leaders reached the accord only days after the Organization of American States, the Western Hemisphere's top diplomatic body, failed to resolve the dispute as Washington backed an otherwise isolated Uribe.

Cuba's ailing Fidel Castro, a Chavez ally, praised Latin American presidents for putting their differences aside and avoiding an outbreak of war and wrote in a column that "(U.S.) imperialism was by all means the only loser."

Friday's outcome confirmed predictions from the Pentagon to Wall Street that the dispute would not escalate into the first military conflict between countries in the region since Peru and Ecuador fought briefly over their border more than a decade ago.

The resolution also resurrected hopes for the release of FARC hostages, including a French-Colombian woman and three Americans. Chavez, who had negotiated the freeing of six captives in the weeks before the crisis, announced at the summit he had new proof more captives were alive.

"I hope there can be releases soon," said Venezuelan Interior Minister Ramon Rodriguez, who coordinated the previous deals.

With the dispute resolved, Venezuela and Nicaragua immediately restored ties with Colombia.

Anticipating sending his envoy back to Managua, Uribe quipped to his Nicaraguan counterpart, "I'll send you the bill for the ambassador's airfare." (Additional reporting by Manuel Jimenez in Santo Domingo, Brian Ellsworth in Caracas and Anthony Boadle in Havana; Writing by Saul Hudson; Editing by Peter Cooney)

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