Taoiseach Micheál Martin says he accepts that Agriculture Minister Barry Cowen is genuinely remorseful for his driving ban.
Mr Cowen had a three month ban for drink driving while on a provisional licence in 2016.
He is set to make a statement to the Dáil on Tuesday on the issue.
Mr Martin says while it is unfortunate, he accepts Minister Cowen is sorry.
"He has articulated his profound regret and sorrow and shame at what transpired four years ago.
"I became aware of this on Friday - it's deeply, deeply regrettable, it shouldn't have happened".
Mr Cowen is facing calls to clarify how long he was driving without a full driver’s licence.
The Offaly TD was disqualified from driving for three months and fined €200 after being detected over the limit while driving home from Dublin.
He also confirmed that he was driving on a learner permit at the time and, while he was not driving unaccompanied when he was pulled over, he had done so previously.
Earlier the founder of the Irish Road Victims Association, Donna Price, said he should step aside from his role.
“I think his position is untenable,” she said.
“Much as I don’t like to kick someone when they are down and when they have made an apology, really it goes further than that and I think it shows a complete disregard for other users.”
She said Minister Cowen showed a complete disregard for the safety of other road users.
“He has broken the law not just by drink driving but also by driving while unaccompanied so that shows a complete disregard for the safety of other road users.
“Those laws are there to protect all of us and so it is simply inexcusable. As I said he could have killed or seriously injured somebody and we don’t appreciate that our public representatives would take such a chance.”
Rise TD Paul Murphy has said he finds it “a bit bizarre” that someone who was almost 50 years old and “presumably drove most days of his life” did not have a full licence.
It comes after Newstalk revealed in May that nearly 5,000 people in Ireland had been driving with only a learner permit for over 20 years.
According to the Freedom of Information figures, nearly 240,000 drivers across the country were on learner permits.
Nearly 23,000 drivers had a learner permit for at least ten years, nearly 5,000 had one for more than 20 years and 1,442 had one for over 25 years.
Penalty points were issued to almost 2,000 learner drivers last year for driving without a fully qualified driver in the car with them.