*Betancourt, 3 Americans, 11 other hostages rescued
*Minister says government tricked guerrillas
*Betancourt, weeping, thanks Colombian military
*Bush congratulates Uribe
*U.S. ex-hostages in American hands
By Hugh Bronstein
BOGOTA, July 2 (Reuters) - French-Colombian politician Ingrid Betancourt, three Americans and 11 other hostages held for years in jungle captivity were rescued on Wednesday from leftist guerrillas by Colombian troops posing as aid workers.
The rescue was a huge coup for popular President Alvaro Uribe, an anti-guerrilla hard-liner who has used billions of dollars in U.S. aid to push the rebels onto the defensive, cut crime and spur economic growth.
Betancourt, 46, was the highest profile captive held by the Revolutionary Armed Forces of Colombia, known as the FARC, Latin America's oldest surviving left-wing insurgency.
A former presidential candidate, her dual French-Colombian nationality had helped bring world attention to the plight of hostages held by the rebels.
"I believe that this is a sign of peace for Colombia, that we can find peace," Betancourt said, thanking the Colombian military for her rescue and weeping as she made her first public comments, carried on Colombian radio station Caracol.
Minutes later a pale but smiling Betancourt landed in Bogota's military air base, walking down the stairs of the plane and hugging her mother, Yolanda Pulecio, who was waiting on the runway.
Defense Minister Juan Manuel Santos said all of the former captives were in reasonably good health despite having been held in harsh conditions, often chained by the neck by their rebel captors.
The rescue was carried out in the southern jungle province of Guaviare, Santos said. Soldiers posed as members of a fictitious non-government organization that supposedly would fly the hostages by helicopter to a camp to meet with rebel leader Alfonso Cano.
"The helicopters, which in reality were from the army, picked up the hostages in Guaviare and flew them to freedom," Santos said. Two guerrillas were captured in the operation.
Fifteen long-term kidnap victims were rescued in all, including Betancourt and the three Americans, he said.
"It (the rescue) will go down in history for its audaciousness and effectiveness," Santos told reporters.
The FARC has been holding about 40 high-profile hostages it has sought to exchange for jailed rebels.
BETANCOURT AT MILITARY BASE
French President Nicolas Sarkozy said Betancourt was in good health and despatched his Foreign Minister, Bernard Kouchner, in a plane to Colombia.
"Today a nightmare of more than six years has ended," Sarkozy said at the presidential palace.
The president's office said earlier that Sarkozy had had a long conversation with Uribe. France had made vigorous efforts to seek Betancourt's freedom.
Betancourt was kidnapped by the FARC in 2002 and was last seen in a rebel video at the end of last year looking ill, gaunt and despondent.
"I am filled with happiness," Betancourt's sister, Astrid, told Colombian radio. "These have been long years of waiting."
The freed Americans are former Defense Department contract workers Marc Gonsalves, Keith Stansell and Thomas Howes. All three worked for Northrop Grumman and were captured in 2003 after their light aircraft crashed in the jungles while on a counternarcotics operation.
U.S. President George W. Bush spoke by telephone with Uribe.
"President Bush congratulated President Uribe, telling him he is a 'strong leader.' President Uribe thanked President Bush for his support and confidence in the Government of Colombia," Gordon Johndroe, White House National Security Council spokesman, said in Washington.
Northrop Grumman said in a statement that the three Americans had been transferred to the custody of the U.S. government in Colombia for return to the United States.
U.S. Secretary of State Condoleezza Rice congratulated Uribe and the Colombia military on the rescue of the hostages.
"We are delighted with the safe recovery of these Americans ... We are working now to reunite them swiftly with their families in the United States," Rice said in a written statement.
She urged the FARC to release all other hostages and said the United States held the group responsible for the health and well-being of those still in captivity.
CONDITIONS FOR TALKS
The FARC has demanded that Uribe pull back troops from an area the size of New York City to facilitate talks.
Uribe, whose father was killed in a botched FARC kidnapping years ago, refuses to accept that condition. But he has offered a smaller safe haven under international observation in an area where there are no armed forces or armed groups.
The outlawed rebel army, once a 17,000-member force able to attack cities and kidnap almost at will, has been driven back into remote areas and now has about 9,000 combatants. The guerrillas have lost three major leaders this year.
Listed as a terrorist group by U.S. and European officials, the FARC has used Colombia's cocaine trade to fund its operations.
In announcing the rescue operation, Santos called on the guerrillas to give up their arms and negotiate a truce.
Michael Shifter, an analyst at the Inter-American Dialogue, a Washington-based think tank, said the rescue showed that the FARC was in a serious organizational crisis.
"The Colombian government took advantage of the FARC's weakness and disarray to carry out the mission. It was a big gamble, but it worked," he said.
"Uribe is a risk-taker and is full of surprises. Not that he needs it, but this remarkable turn of events will further boost his popularity."
U.S. Republican presidential candidate John McCain, who had been visiting Colombia, was informed about the successful release of the hostages while en route to Mexico from Colombia.
A spokesman told reporters on McCain's plane that on Tuesday night, Uribe and his defense minister pulled aside McCain and the two senators traveling with him to inform them of the operation that was planned for Wednesday to free the hostages. The three had not learned about the success of the operation before departing Colombia.
(Additional reporting by Emmanuel Jarry and Sudip Kar-Guptain Paris; Adriana Garcia, Tabassum Zakaria and Arshad Mohammed in Washington; Writing by Hugh Bronstein; Editing by Frances Kerry)