The seizure comes after efforts by Hugo Chavez, the Venezuelan president, to broker a hostage deal fell apart, with Colombia suspending his role.
Luis Carlos Restrepo, high commissioner for peace, said on Thursday that other Colombian hostages were allso shown in the five videotapes.
The tapes, which were played at a news conference without sound, showed Betancourt in front of a jungle backdrop.
In one video she looks gaunt and is seen chained and staring at the ground. The government said the tapes carried the date of October 24, 2007.
Speaking to Al Jazeera from Paris, Lorenzo Delloye, Betancourt's son, said: "I was happy to see my mother was alive... we hadn't had news from her since four years.
|"I was happy to see my mother was alive... we hadn't had news from her since four years"|
"The other feeling I had was sadness... to see she was really, really sad, suffering... the reality of someone being held hostage in the Colombian jungle, which is inhuman."
Alvaro Uribe, Colombia's president, said that there were indications that Betancourt had been tortured.
"The video indicates torture, particularly in the case of Dr Ingrid Betancourt and Senator Eladio Perez," hee said.
However, Betancourt's sister Ingrid insisted there was nothing to suggest the former senator had been tortured. She said Uribe's statements had endangered future efforts to have the hostages released.
Another video shows Mark Goncalves, Kein Stambler and Thomas Howes, US contractors who were taken hostage by Farc in 2003, Restrepo said.
This tape carried the date January 1, 2007, although a man believed to be a kidnapped Colombian soldier is heard on the tape saying the date is October 23.
Betancourt was kidnapped in February 2002.
'Proof of life'
Armand Burguet, president of the International Federation of Ingrid Betancourt Committees, told Al Jazeera he and Betancourt's family were "very happy to see this proof of life has finally arrived".
|Three alleged Farc fighters were arrested |
when the videos were seized [AFP]
"It is something the families of the hostages and ourselves have been waiting for a long time," he said.
But he added Betancourt's family were still very upset.
"We don't have a video from Ingrid we just have a video and a letter. In the picture she appears very feeble. She's wearing chains and appears to be in a very bad physical condition," he said.
The Colombian military also seized letters written by the hostages.
One letter dated October 24 was written by Betancourt to Yolanda Pulecio, her mother, authorities said. In another letter, dated November 26, 2006, Howes makes changes to his will.
Betancourt and the three Americans are among about 45 hostages that Farc wants to swap for 500 prisoners from the group.
The failure to release the hostages triggered a diplomatic spat between Alvaro Uribe, Colombia's president, and Chavez earlier this month.
Chavez now says he will have no relations with Colombia while Uribe remains in office.