CARACAS, Venezuela (AP) — Helicopters sent by Venezuela's president picked up two hostages freed by Colombian rebels in the jungle Thursday and flew the women across the border in a mission that could open a new path to freedom for dozens of captives.

Beaming in a forest clearing after six years in captivity, the women kissed the cheeks of heavily armed rebels, who then disappeared in a single-file column into the brush. The women, thin but apparently in good health, were flown to Caracas, where they were embraced by tearful relatives on the tarmac.

"We are being reborn!" Clara Rojas exclaimed.

Venezuelan President Hugo Chavez greeted them with hugs and kisses at the presidential palace. The women and their families stood alongside him and sang Colombia's national anthem. They made no public comments.

Rojas was an aide to Colombian presidential candidate Ingrid Betancourt in February 2002 when the two were kidnapped on the campaign trail. She gave birth in captivity to a boy fathered by one of the guerrillas. Betancourt is still being held.

The other freed hostage, former congresswoman Consuelo Gonzalez, had been abducted in September 2001. During her captivity, her husband died and a grandchild — now 2 — was born to one of her daughters. After getting off the plane, she embraced the child, and Chavez later held the girl in his arms.

Their release was a major triumph for Chavez, whose leftist ideology helped win him a mediation role with the rebels. It was the most important hostage release in the half-century Colombian conflict since 2001, when the Revolutionary Armed Forces of Colombia, or FARC, freed some 300 soldiers and police officers.

Chavez said the mission demonstrated that "there are possibilities" to secure the release of some of the more than 700 prisoners believed being held by the FARC, including Betancourt and three American defense contractors.

Rojas said the two were carrying "proofs of life" — usually letters and videos — from 10 other hostages, some of whom haven't been heard from in years.

"Venezuela will continue opening the way for peace in Colombia," Chavez said. "We are ready, and in contact with the FARC, and we hope the Colombian government understands. I'm sure they will understand."

The release could help the flamboyant Chavez take on a greater role in Latin America's longest-running conflict, in spite of increasingly hostile relations with Colombia's U.S.-allied president, Alvaro Uribe. The release puts pressure on Uribe for government concessions to secure the release of 44 other high-profile captives.

Betancourt holds both Colombian and French citizenship, and France's government was cheered by Thursday's hostage release.

"This proves that things are moving, that the mobilization is bringing its first results," said President Nicolas Sarkozy of France, which has campaigned for Betancourt's release. "This commits us to boosting our efforts to bring the other hostages home."

Rojas said she hadn't had contact with Betancourt since they were separated by the rebels for security reasons three years ago.

"But I trust that soon she'll be here with us," Rojas told Caracol. "Take heart, Ingrid. I hope to see you here soon."

The guerrillas have offered to exchange the 44 high-profile hostages for hundreds of rebel fighters imprisoned in Colombia and the United States.

Chavez was trying to negotiate such an exchange in November when Uribe called him off, saying the Venezuelan leader improperly made direct contact with the head of Colombia's army. Chavez responded by freezing relations with Uribe.

The FARC offered last month to release the two woman directly to Chavez, along with Rojas' 3-year-old son, Emmanuel. But that deal fell through Dec. 31 when the FARC accused Colombia of conducting military operations in the area of the planned release.

Uribe's government said the guerrillas backed out because they didn't have the child — a theory later proved by DNA tests that confirmed Emmanuel has been in a Bogota foster home for more than two years.

Rojas said her son was taken away from her eight months after his birth and she didn't receive news of him again until three years later, this New Year's Eve, when Uribe said the boy had been living in a foster home. Rojas said she hopes to be reunited with Emmanuel soon.

"I was always very worried to know where my baby was," she told Colombia's Caracol Radio.

Rojas' elderly mother, Clara Gonzalez de Rojas, was overcome with emotion as she hugged her daughter for the first time since 2002.

"I'm living a dream. I don't have words to describe it," she said in a quavering voice.

Chavez asked the news media to respect the released hostages' privacy. But Venezuela's state-supported television network Telesur broadcast video of the prisoner handover, complete with gushing statements of gratitude from the hostages to Chavez.

"President, a thousand thanks for your humanitarian gesture," Gonzalez was shown telling Chavez by satellite phone.

Hours later, they met with him at the palace in Caracas. Chavez saw the women off with hugs and kisses as they left with their families, who have been waiting in a Caracas hotel for weeks.

The State Department welcomed the hostages' release and reiterated its call for FARC to release all of its hostages.

The head of the European Union's administrative body, Jose Manuel Barroso, called the women's freedom "an encouraging sign that all detained hostages, including Ingrid Betancourt, will be released soon."

Colombian Vice President Francisco Santos, who once was held hostage by a criminal gang for eight months, applauded the release, but added: "Let's not forget the more than 750 other hostages being held by the FARC, some held for more than 10 years, about whom we know nothing."