VILLAVICENCIO, COLOMBIA (CNN) -- A mission to free three hostages held by leftist rebels in Colombia stalled Monday, with the rebels and Colombian authorities trading blame for the delay.
On Monday night, President Hugo Chavez of Venezuela, who organized the mission, said he remained hopeful that the operation would succeed despite major obstacles that surfaced earlier in the day.
"There is no deadline," he told reporters Monday night.
The leftist Revolutionary Armed Forces of Colombia, known as the FARC for its Spanish acronym, had planned to release three hostages as part of a deal Chavez brokered. Yet they reversed course Monday and said that Colombian military operations in the area made a release impractical.
"Due to the intense military activity in the zone, the FARC is prohibited and unable to give up the hostages due to fear for their safety and the safety of any guerrilla members involved in the operation," the group said in a statement Chavez read to reporters. "As soon as there is certainty of a safe place for the release of the hostages, this one will take place."
In a televised news conference from Villavicencio, Colombia, Colombian President Alvaro Uribe denied the group's assertion and said there are no combat operations in the area near the rebels. He blasted the FARC as a terrorist organization with a history of kidnapping and killing.
"The FARC has always deceived Colombia, and they want to deceive the world," Uribe said.
The sharp exchanges cast doubt on the future of "Operation Emmanuel," a mission to free Clara Rojas, who managed a candidate's bid for the Colombian presidency in 2002; her son, Emmanuel; and Consuelo Gonzalez, a prominent Colombian politician.
The FARC kidnapped Rojas and Gonzalez in 2002. Rojas gave birth to Emmanuel in 2004. He is apparently the result of a relationship she had with a rebel, but the nature of that relationship is unclear.
On Monday night, Chavez expressed hope that the mission could still succeed. He told reporters that Venezuelan helicopters would continue to wait in central Colombia for further instructions from the FARC as long as the Colombian government allowed them to.
Meanwhile, people in Colombia and Venezuela were digesting a stunning suggestion from Uribe that the FARC delayed releasing the hostages because they don't actually have custody of the three-year-old captive.
Authorities in Colombia suspect that the FARC duped child-welfare authorities in Colombia by presenting the boy as a child in need of foster care in 2005, he said.
"The FARC has not dared to move forward on their commitment to liberate the hostages because they do not have in their custody the child, Emmanuel," the president said.
Investigators have identified a boy who could be Emmanuel -- he's in a foster home in Bogota, Uribe said -- and authorities have asked the Red Cross to conduct DNA tests on Emmanuel's grandmother. Those tests could confirm or refute their suspicions.
During his news conference, the Colombian president blasted the FARC for violating international norms and kidnapping and killing several hostages in the past. The Colombian government had given all necessary assurances for the successful completion of the mission, Uribe said.
Two Venezuelan helicopters -- which carried the symbol of the International Committee of the Red Cross -- and their crews waited in vain over the weekend in Villavicencio to receive coordinates from the rebels. A team of international delegates formed by Chavez and charged with overseeing the hostages' release are also in Villavicencio. They include Latin American diplomats and politicians, as well as U.S. movie director Oliver Stone.
Uribe had originally asked Chavez to help secure the release of hostages, hundreds of whom are held by the FARC and the National Liberation Army (ELN). But last month, Uribe effectively fired Chavez, saying he broke protocol by communicating directly with his top general. Chavez has since called Uribe a "liar" and said FARC was ready to release prisoners, but Uribe's interference stalled those plans.
FARC's promise to release the three hostages has been seen as an effort to get Chavez back on board as a mediator -- the Venezuelan president is more sympathetic to the rebels than Uribe's government -- and a positive public relations move during the holidays.
The FARC has justified hostage-taking as a legitimate military tactic in a long-running and complex civil war that has also involved right-wing paramilitaries, government forces and drug traffickers. Fighting has waned, but not stopped in recent years.
The planned release of the three hostages stirred hope that the FARC could free others in captivity.
Among the captives are three American contractors who were captured when their plane went down in 2003 during a drug-eradication flight, and Ingrid Betancourt, a French-Colombian independent presidential candidate who was kidnapped in 2002. Rojas was kidnapped in 2002 while she managed Betancourt's campaign.
Betancourt herself is perhaps the best-known captive in a country plagued by kidnapping. Her release has become a cause celebre in France. Earlier this month, French President Nicolas Sarkozy appealed to FARC to release Betancourt, saying he had a "dream to see Ingrid among her family this Christmas."
Established in 1964 as the military wing of the Colombian Communist Party, FARC is Colombia's oldest, largest, most capable and best-equipped Marxist rebel group, according to the U.S. Department of State. The United States, the European Union and Colombia classify FARC as a terrorist group. E-mail to a friend
CNN's Karl Penhaul contributed to this report.