By Hugh Bronstein

BOGOTA, Nov 1 (Reuters) - Colombian President Alvaro Uribe has said he may run for a third term if his coalition fails to unite around a strong candidate, prompting debate on Thursday about the future of democracy in the conflict-weary country.

Uribe, an important U.S. ally in the left-tilting Andean region, won a second four-year term last year after the constitution was changed to allow one re-election.

Many want him to run again in 2010 while others fear such a move would put Colombia on an authoritarian path.

The bespectacled Wall Street favorite shocked supporters and opponents alike by telling members of Congress in a private meeting late on Wednesday that he would be open to a third campaign if there was a "catastrophe."

"The coalition has to find another candidate. Re-election only if there is a catastrophe," lawmaker Nancy Gutierrez, an Uribe ally at the meeting, quoted the president as saying.

Presidential adviser Jose Obdulio Gaviria told local radio that the "catastrophe" would come if Uribe's supporters cannot rally around one candidate to carry on his legacy.

"Without unity there will be a catastrophe," he said.

Opposition politicians took to the airwaves saying a third term would put Uribe in the same category as Hugo Chavez, the leftist anti-American leader of neighboring Venezuela who wants to scrap presidential term limits.

Polls show Uribe would win if the law is changed to allow him a third campaign.

Seen as a savior by millions of Colombians traumatized by decades of guerrilla war, he has cut urban crime and spurred investment with his U.S.-backed crackdown on drug-running leftist rebels.

"Uribe's statement confirms that all those Colombians who fear the day he leaves office may get the chance to vote for him again," said pollster Napoleon Franco.

Opponents say he is too cozy with right-wing paramilitary militias that have demobilized under a government peace deal offering reduced jail terms for crimes ranging from extortion to massacre to cocaine trafficking.

Uribe remains popular despite a scandal in which dozens of members of his coalition, including his senator cousin Mario Uribe, are being investigated for illegal dealings with paramilitary thugs.

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