Uni gave a letter to a journalist to be delivered to Betancourt's mother, Yolanda Pulecio, who is supposed to pass it to Nicolas Sarkozy, the French president.
"I admire her very much," he said of Pulecio, adding that Betancourt's abduction was never planned.
"The order was to detain all politicians of national stature."
Uni said Betancourt was surprised to learn that she was dealing with the Revolutionary Armed Forces of Colombia, or Farc, and not the military as she had presumed.
|The Farc wants to swap high-profile hostages|
for hundreds of jailed rebels [EPA]
"Her face changed colour," he said. "She didn't say anything to me."
Uni said he was in charge of the roadblock on the day of the abduction and was only with Betancourt for a day before she was handed over to fellow rebels.
Concerns for Betancourt's welfare have increased since hostages who spent time with her and were recently released said she was depressed and suffering from hepatitis B.
Her family in Paris declined to comment on the apology but said there was no basis for reports that she has hepatitis B and is near death.
On Tuesday Betancourt's sister, Astrid, told The Associated Press that it is likely her captive sibling has a parasitic infection and could be malnourished.
"What is crystal clear for me is that my sister is weak," she said, referring to discussions with physicians and freed hostages who saw Betancourt on February 4.
"But that doesn't mean that she is so ill she's on the brink of death. Nor does it mean that she's on a hunger strike as some people in France have said."
The French government has pledged to continue efforts to free Betancourt after a humanitarian mission sent this month to treat or rescue her and other hostages held by Farc had to be called off after the rebels rejected the plan.
Betancourt, who was snatched by Farc in February 2002, is the most high-profile of around 40 "political" hostages the group is holding in hopes of a swap for 500 of its own members in Colombian and US jails.
The Farc is also holding hundreds of other Colombian hostages as part of what it has said is a Marxist armed struggle against the Colombian government.