"It is clear that breaches of public health guidelines were made by commissioner Phil Hogan since he travelled to Ireland", Mr Martin and Mr Varadkar said.
The Irish Government believes that Mr Hogan breached public health restrictions - a claim denied by the former Fine Gael Cabinet Minister.
On Tuesday, Mr Hogan provided details to the President of the European Commission, Ursula von der Leyen, about his time in Ireland leading up to his attendance at the Oireachtas Golf Society event.
In hindsight I was wrong and made a mistake...and I apologise for it.
"I was asked to give a fuller account by the president, in fact I was asked by the Taoiseach... and I hope people will see I've done everything possible in order to comply with the COVID-19 regulations".
This morning Eamon Ryan said the government has lost confidence in the Commissioner, but says it will respect the decision from Brussels.
In a joint statement, the leaders of the Republic of Ireland's governing coalition said the commissioner had clearly breached guidelines and he should have restricted his movement for 14 days.
United States tries to overrule UN Security Council in sanctioning Iran
After 30 days, all of the United Nations sanctions previously placed on Iran would "snap back" into place. Ambassador Majid Takht Ravanchi speaks to reporters at U.N. headquarters in New York, Aug. 20, 2020.
Referring to the Oireachtas Golf Society dinner, he added: "I fully accept that it is abundantly clear that the event should not have been held and that I should not have attended this dinner".
"Our webpage on Testing for Covid-19 covers information for people in Ireland who may need to be tested for Covid-19", Citizen's Information said in a statement.
The European Commission President has spoken further with the embattled Commissioner after he issued her with a report on his movements in Ireland and a decision on his future in the position is expected today.
The question now is who will replace him and will Ireland keep that portfolio?
"We were there for our wedding anniversary; he was seated at the table behind us with two other gentlemen", she said.
His departure creates another problem for Von der Leyen, who will need to find a replacement, amid hard trade talks with America, China and the UK.