Sgt Robinson Salcedo has been held since 1998
Colombian television has broadcast footage of 10 soldiers and policemen held captive by left-wing Farc rebels for at least 10 years.
In the videos, the men are seen bound around the neck by chains as they speak directly to their families and make an appeal for their release.
The videos are the third set to emerge in recent weeks.
The Farc want to swap hostages in turn for imprisoned rebels, a move President Alvaro Uribe has rejected.
The videos, each lasting about 90 seconds, show the four soldiers and six police officers sitting in front of a cloth designed to disguise their location, with a chain padlocked around their necks.
The hostages, kidnapped in 1998 and 1999, look tired and haggard.
"Thank you to all Colombians for your support - all those working to secure our release as soon as possible," says Sgt Robinson Salcedo Guarin.
"I'm in good health," says police officer Jorge Trujillo, who also urges his mother not to cry when she sends messages to him via Colombian radio stations.
Mr Trujillo rocks back and forth and he appears disoriented in the footage.
"Our situation is difficult and we need to get out as quickly as possible," says Police Sgt Jose Libardo Forero.
A government statement deplored the "lamentable conditions" in which the men were being held and called for their "total and unconditional release".
Unlike the two previous videos, which were released via a Colombian politician involved in efforts to secure the hostages' freedom, the latest footage was seized from a Farc operative at a military checkpoint, Air Force commander Gen Freddy Padilla said.
The military high command said the videos constituted "proof of cruel and degrading treatment" of the prisoners by the Farc.
The guerrillas have agreed to free many of the hostages unilaterally, as they have done with six in the past, but the government has insisted it wants them all freed at once.
Some families of the hostages are pressing for the authorities to reverse their decision not to negotiate with the rebels.
While the release of proof-of-life videos and statements by the Farc is designed to put pressure on Mr Uribe to negotiate, the Colombian president, who has pursued a hard line with the rebels, enjoys approval ratings of over 50%.
He may seek a third consecutive term, if moves to change the constitution to allow presidential re-election are approved by the courts and backed in a referendum.