By Hugh Bronstein

BOGOTA, March 5 (Reuters) - Latin America's one-time 'odd couple' is in no mood for hugging.

A simmering dispute between Hugo Chavez and Alvaro Uribe, the hard-willed, politically opposed presidents of Venezuela and Colombia, has exploded into diplomatic dog-fight that threatens to destabilize the region.

The crisis erupted after Colombian forces entered Ecuador on Saturday to kill a Colombian rebel leader.

Uribe charges leftist allies Ecuador and Venezuela with supporting the guerrillas; Chavez and Ecuadorean President Rafael Correa have cut diplomatic ties with Colombia and sent troops to their neighbor's border, vowing to meet any future incursions with force.

The military and diplomatic hostilities have blown away a once-chummy relationship between fiery leftist Chavez and the conservative, studious-looking Uribe.

For years they appeared to get along so well they were dubbed the odd couple of Latin American politics. They were seen hugging and chatting amiably at public events as they seemed to set aside ideological differences, focus on trade ties and bond on common personality traits.

Chavez, who first won office in 1998, and Uribe, in power since 2002, both enjoy high popularity at home, like to micromanage government affairs and are given to folksy town hall-style speeches. Each has clinched constitutional permission to run for extra time in office.

But tension simmered under the surface as Uribe confirmed his place as Washington's chief ally in South America and former coup-leader Chavez, loved by many poor Venezuelans for his generous oil-export-funded social programs, called for region-wide revolution.

"For diplomatic and short-term political reasons they decided to create a relationship which frayed very quickly. Now they've gone back to being what they are," said Riordan Roett, Latin American studies director at Johns Hopkins University.

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As recently as October last year it had looked as though Chavez and Uribe were getting closer than ever after Uribe invited the Venezuelan leader to broker a deal with the Revolutionary Armed Forces of Colombia, or FARC.

Under the deal, rebel-held hostages such as French-Colombian politician Ingrid Betancourt would be swapped for jailed rebels. Chavez would have used his sway with the guerrillas to help resolve a long-running sore for Colombia.

Uribe, whose father was killed in a botched guerrilla kidnapping more than 25 years ago, pulled that invitation and fell out with Chavez in November after saying the Venezuelan overstepped his bounds as hostage mediator.

Chavez called Uribe a "pawn of the (U.S.) empire" better suited to being a "Mafia boss" than president.

Uribe this week accused Chavez of sponsoring and financing genocide in Colombia by giving money to the FARC.

"You get the feeling that the two started really saying what they felt in November, and it's been so cathartic its been hard for them to stop," said Adam Isacson, Colombia expert at the Center for International Policy.

For years Colombian officials said privately that they suspected Chavez was allowing the FARC to use Venezuela as a safe haven.

Venezuelan officials meanwhile whispered that they suspected Uribe of being a right-wing paramilitary criminal.

Analysts say most Colombians back Uribe in the current dispute while the effect on Chavez's popularity will depend on the outcome. Meanwhile the verbal barbs are expected to continue.

"One is a successful, conservative politician trying to run a country in the middle of a civil war. The other is a pushy populist who can't keep his mouth shut and who has been meddling in his neighbor's back yard," Roett said. "Uribe is calling his bluff."

(Reporting by Hugh Bronstein, Editing by Frances Kerry)

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