Phil Hogan was stopped by gardaí for using his mobile phone while driving in Kildare before attending the Oireachtas Golf Society dinner in Clifden last week.
A spokesperson for the Ireland's EU Commissioner told RTÉ the incident happened on August 17 while Mr Hogan was en route from Kilkenny to Kildare collect "personal belongings and essential documents" at his apartment there before driving on to Galway.
EU trade commissioner Phil Hogan has issued a "fulsome and profound" apology as calls for him to quit after attending a golf dinner during the pandemic intensify.
Mr Hogan has been urged to consider his position by the leaders of the Republic's coalition Government, Micheal Martin and Leo Varadkar, after the event at a hotel in the west of Ireland with more than 80 people present.
He is seen as having significant standing in Brussels, a politician who would be deeply involved in any deal with Britain after Brexit.
In a statement he said: "I acknowledge my actions have touched a nerve for the people of Ireland, something for which I am profoundly sorry.
"I realise fully the unnecessary stress, risk and offence caused to the people of Ireland by my attendance at such an event, at such a difficult time for all, and I am extremely sorry for this."
Gardaí are investigating whether coronavirus regulations were broken in holding the Oireachtas Golf Society event two days after the Government announced it intended to curb the numbers permitted to gather together.
A resurgence in Covid-19 cases in recent weeks has led the Government to backtrack on some of its plan to reopen society after lockdown.
The function was held across two rooms in the hotel in Clifden. Other attendees including, the then agriculture minister Dara Calleary and Jerry Buttimer, Leas Cathaoirleach of the Seanad, have resigned.
Supreme Court judge Seamus Woulfe was among others on the guest list.
Mr Hogan said: "I acknowledge that the issue is far bigger than compliance with rules and regulations and adherence to legalities and procedures.
"All of us must display solidarity as we try to stamp out this common plague.
"I thus offer this fulsome and profound apology, at this difficult time for all people, as the world as a whole combats Covid-19."
He paid tribute to the "wonderful" healthcare workers who continue to put their lives on the line to combat Covid-19, and to everyone who has lost a loved one during the pandemic.
A Government statement said Mr Martin and his deputy Mr Varadkar "both believe the event should never have been held, that the commissioner's apology came late and that he still needs to give a full account and explanation of his actions".
Mr Hogan is the EU's former agriculture commissioner and oversaw significant reform of the Common Agricultural Policy.
Trade is a central issue in the EU's efforts to build agreement with the UK to mitigate any ill-effects from Brexit.
The commissioner is a native of Kilkenny in the south east of the country and a former Irish environment minister for Fine Gael.
It is the EU Commission president who would have to force his resignation.
Mr Varadkar told RTÉ Radio 1 the apology had helped but Mr Hogan should go further and explain his movements around Ireland.
He said: "He needs to answer any questions people have got about the dinner and also his movements within the country and in and out of Kildare."
Kildare, where the commissioner has a property, has been subjected to local pandemic restrictions due to an elevated number of Covid-19 cases.
Mr Varadkar expressed confidence in Mr Hogan's ability to do his duty as trade commissioner and said he has done a good job in that post so far.
"It is our view that an apology is welcome but he also needs to account for himself and explain and answer any questions that might arise, not just in relation to the dinner but also his movements around the country.
"If he cannot do that he needs to consider his position," he added.
Sinn Féin president Mary-Lou McDonad said the commissioner's position was untenable.
"It is very clear that he has lost the confidence of the Government, the Taoiseach and Tánaiste have asked him to consider his position.
"That really means game over.
"It would be very, very alarming and would deepen the sense of crisis and chaos if the commissioner were to stay on despite having lost the confidence of the Taoiseach and Tánaiste."