The images do not show the subduing of two members of the Revolutionary Armed Forces of Colombia (Farc) who were on the helicopter used to fly the hostages to a Colombian military base.
The video was shot by Colombian soldiers posing as a media crew during
Wednesday's daring operation, in which the military fooled the rebels into releasing the captives into their custody.
In the images, some of the former hostages - including three US Pentagon contractors and 11 Colombian policemen - are seen arguing with the Farc rebels and Colombian soldiers as they were handcuffed before entering the helicopter.
The camera zooms in on American Keith Stansell, who is seen telling the camera: "I love my family ... pray a lot."
Betancourt is in a French hospital for health checks following her six year ordeal as a hostage of Colombian rebels.
She is believed to have developed a string of ailments during her time in captivity, possibly including hepatitis, although she told reporters on Friday, that she was "in great shape".
|Betancourt had an emotional reunion
with her children on Thursday [AFP]
The videotape was displayed at Colombia's military headquarters in the capital, Bogota, on Friday.
The tape's release comes shortly after Betancourt, who was held captive by the Farc for six years, arrived in France and was met by Nicolas Sarkozy, the French president, and Carla Bruni, his wife.
She said on her arrival that she had "cried many times in pain, indignation, now I cry in joy".
Betancourt, who grew up, studied and raised her children in Paris, said that she had "dreamed of this moment for seven years".
She praised the "extraordinary Colombian heroes" who had rescued her and also thanked Sarkozy for his efforts in securing her freedom.
The French president, who was visibly moved, said: "Ingrid Betancourt, welcome. France loves you."
On Friday, Juan Manuel Santos, the Colombian defence minister, denied media reports that Israel was involved in the operation, saying "not a single foreigner participated".
However he said US authorities were informed 10 days before the operation as
part of an agreement Alvaro Uribe, the Colombian president, had with George Bush, his US counterpart.
Colombian officials also denied that a ransom had been paid for the hostages' release.
At a news conference on Friday, Betancourt said she doubted a Swiss radio report which said that Farc members were paid up to $20m to release her and the others in a deal brokered by the US.
The report said that the wife of one of the guards was the go-between, having been arrested by the Colombian army. She was released to return to Farc, where she persuaded her husband to change sides.
"Given what I saw during the operation - and frankly, honestly, I don't think I can be easily fooled - I don't believe that what I saw was a set-up," Betancourt said.
Betancourt also appealed to Sarkozy on Friday for help in freeing thousands of other hostages who remain in Colombia's jungles.
"I still need you, because we cannot leave them where they are," she said at a party in her honour at the presidential palace. "They are suffering, they are alone."
The Farc group, which has been battling the Colombian government for decades, is thought to hold about 30 foreign captives and hundreds more Colombian civilians and security forces members.
The rescue operation is thought to have further damaged the group, which has already been hit by the deaths of several senior leaders and desertions from its ranks.