Mr Barry said there was no excuse for what he did.
"What I did last night was disrespectful and inappropriate," he said.
"I have apologised to Aine Collins and she graciously and immediately accepted my apology. No excuses, I just shouldn't have done it."
Mr Barry and Ms Collins, both from Fine Gael, were caught on camera in the Dail chamber when he pulled her onto his lap.
The pair could be seen talking before Mr Barry holds his fellow Cork TD by the hips and puts her on his knee. After a few seconds she shrugs him off and walks up a flight of stairs.
The party said the incident was light-hearted but insensitive, and should not have happened.
"Obviously, it's regrettable that it happened. It probably should not have happened," a spokeswoman said.
"The deputies are good friends and there was no malice involved."
It is understood no offence was taken by Ms Collins and none had been intended by Mr Barry.
Both were elected to the Dail parliament for the first time in 2011.
Other politicians standing in front of Government benches could be seen looking at the pair during the brief incident.
The video clip, from about 2.30am in the morning as debates on the abortion legislation continued through the night, was broadcast on television and online and has since gone viral.
In a separate incident, a Labour politician Michael McNamara voted "incorrectly" on one amendment as debate on the legislation drew to a close at 5am.
The Dail record cannot be changed but it is understood Mr McNamara will not face any sanction.