Presidential candidate Gavin Duffy has claimed that RTÉ is a "fan club" for President Michael D Higgins.
He was criticising the incumbent's role in "building bridges" in the North, when he was challenged by the presenter.
"President Mary McAleese did huge work building bridges building bridges north and south, east and west. I'd have to say our incumbent didn't follow on that work," said Mr Duffy.
"Sometimes we dismiss these positions as ceremonial, [but] the queen just bowing in the Garden of Remembrance did a lot more than a lot of political speeches would have done.
"That's just a fact. I know RTÉ is a fan club for the president..."
Mr O'Rourke cut across the candidate - "Hold it right there" - and asked him to back-up the claim.
In the following exchanges, Mr Duffy said: "RTÉ paid out a large amount of money, so large they were embarrassed to tell us what it was, after the debate in the last election.
"When somebody in the control room is saying 'we've got him', that's the evidence.
"Why is the settlement secret?"
Mr O'Rourke replied: "Because that's what was agreed in court. I don't know the answer to that question."
He added that the situation was "badly screwed up and everybody was deeply embarrassed about it".
Mr Duffy also said the country needs a president with the energy for a "major diplomatic offensive in the UK".
"I would have the energy because I believe if we don't get the [Brexit] deal hammered out fairly quickly in the second half of next year, our economy is going to have serious problems. We don't have room for wobble in our economy."
You can hear the full exchange 20-and-a-half minutes into the below recording of the interview.