Colombian spies tricked leftist rebels into handing over kidnapped presidential candidate Ingrid Betancourt and three U.S. military contractors Wednesday in a daring helicopter rescue so successful that not a single shot was fired.

Betancourt, who was seized on the campaign trail six long years ago, appeared thin but surprisingly healthy as she strode down the stairs of a military plane and held her mother in a long embrace. She said she still aspires to the presidency.

"God, this is a miracle," Betancourt said. "Such a perfect operation is unprecedented."

Eleven Colombian police and soldiers were also freed in the rescue, the most serious blow ever dealt to the 44-year-old Revolutionary Armed Forces of Colombia, which considered the four hostages their most valuable bargaining chips. The FARC is already reeling from the deaths of key commanders and the loss of much of the territory it once held.

The Americans _ Marc Gonsalves, Thomas Howes and Keith Stansell _ were flown directly to the United States to reunite with their families and undergo tests and treatment at Brooke Army Medical Center in San Antonio, Texas.

They had been the longest-held American hostages in the world, according to the U.S. Embassy in Bogota.

Defense Minister Juan Manuel Santos said military intelligence agents infiltrated the guerrilla ranks and led the local commander in charge of the hostages, alias Cesar, to believe they were going to take them to Alfonso Cano, the guerrillas' supreme leader.

The hostages, who had been divided in three groups, were taken to a rendezvous where two disguised MI-17 helicopters piloted by Colombian military agents were waiting. Betancourt said her hands and feet were bound, which she called "humiliating."

At first she thought the pilots were from a relief organization. Then she saw their Che Guevara shirts and assumed they were rebels.

Only when they were airborne did she notice that Cesar, who had treated her so cruelly for so many years, was naked and blindfolded on the floor.

"The chief of the operation said, `We're the national army. You're free,'" she said. "The helicopter almost fell from the sky because we were jumping up and down, yelling, crying, hugging one another. We couldn't believe it."

The operation, Santos said, "will go into history for its audacity and effectiveness."

"We wanted to have it happen as it did today," added armed forces chief Gen. Freddy Padilla. "Without a single shot. Without anyone wounded. Absolutely safe and sound, without a scratch."

Although officials said everyone directly involved in the rescue were Colombians, U.S. Ambassador William Brownfield said there was "close cooperation" from the Americans that included "exchange of intelligence" as well as "exchange of equipment, training advice and experiences of other operations. I will not enter into details."

Santos said Cesar and another rebel on board would face justice. The other rebel captors retreated into the jungle, he said, and the army let them escape "in hopes that they will free the rest of the hostages," believed to number about 700.

At a Bogota ceremony with top military commanders, the freed hostages walked up to a microphone one by one, identified themselves by name and rank, and thanked their rescuers. Some had been held for a dozen years, captured when rebels overran military outposts.

Last to speak was the French-Colombian Betancourt, who wore military fatigues and a floppy camouflage hat as she hugged her mother, Yolanda Pulecio, and her husband, Juan Carlos LeCompte. She removed her hat to reveal intricately braided dark hair, with plaits framing her face and a white flower.

Breaking into tears, Betancourt appealed to the FARC to release the remaining hostages and make peace.

She thanked Colombian President Alvaro Uribe, against whom she was running when she was kidnapped, and said he "has been a very good president."

However, she said, "I continue to aspire to serve Colombia as president."

For now, she added, "I'm just one more soldier."

In Paris, her son Lorenzo Delloye-Betancourt called her release "the most beautiful news of my life." He and other relatives were flying to Colombia to join her.

The Americans appeared healthy in a video shown on Colombian television, though Brownfield, who met with them at a provincial military base, said two of the three _ he didn't specify which _ were suffering from the jungle malady leishmaniasis and "looking forward to modern medical treatment."

Gonsalves' father George was mowing the yard of his Hebron, Connecticut, home when an excited neighbor relayed the news he had seen on television: "I didn't know how to stop my lawnmower. I was shocked. I couldn't believe it."

"We're still teary-eyed and not quite have our wits about us," said Stansell's stepmother Lynne in Miami.

And Howes' niece in Massachusetts, Amanda Howes, says the rescue "redefines the word miracle."

Santos renewed the government's offer to negotiate with the reeling rebel movement, who many believe is nearing the end of its four-decade fight. Battlefield losses and widespread desertions have cut rebel numbers in half to about 9,000 as the United States has poured billions of dollars in military aid into Colombia.

In March, historic leader Manuel Marulanda died of a reported heart attack, and two other top commanders were killed. The rest are hunkered down in remote jungle and mountain hideouts, unable to communicate effectively, their income from ransom kidnappings and the cocaine trade depleted by intense military operations.

Santos said Colombia had infiltrated the rebels' seven-man ruling secretariat, but did not elaborate.

"The government reiterates to them that if they want to enter into serious negotiations in good faith, we are offering a dignified peace," Santos said.

U.S. President George W. Bush called his close ally Uribe to congratulate him, as did French President Nicolas Sarkozy.

U.S. presidential candidate John McCain said Uribe had told him in advance of the rescue plans while he was campaigning in Colombia. "It's a very high-risk operation," he said. "I congratulate President Uribe, the military and the nation of Colombia." His rival, Barack Obama, issued a statement congratulating Uribe as well.

Betancourt, 46, was abducted in February 2002. The Americans were captured a year later when their drug surveillance plane went down in rebel-held jungle. In the five years since, their families had received only two "proof of life" videos, the latest in November.

That tape also showed the first images since 2003 of Betancourt. Along with letters and reports from other hostages, they showed a once-vibrant, confident woman slowly succumbing to Hepatitis B, tropical skin diseases and depression. One former hostage said Betancourt was kept chained to a tree after trying to escape.

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Associated Press writers Vivian Sequera in Bogota, Beth Fouhy with the McCain campaign and Stephen Singer in Hebron, Connecticut contributed to this report.