The Irish government has said it is clear EU trade commissioner Phil Hogan breached coronavirus health guidelines after returning to the Republic.
He has faced criticism for attending a golf dinner with more than 80 people, and for not complying with quarantine rules on arrival from Brussels.
The leaders of the coalition government in Dublin have welcomed an apology from Mr Hogan, but said concerns remained.
Earlier, Mr Hogan published a timeline of his movements in Ireland.
He 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 County Galway on 19 August.
However, three party leaders said Mr Hogan's "delayed and hesitant release of information has undermined public confidence".
In the documents, Mr Hogan said he tested negative for Covid-19 during a hospital visit on 5 August.
He said this meant he was "not under any subsequent legal requirement to self-isolate or quarantine".
However, Ireland's Department of Health has said a person is required to restrict their movements for 14 days if they arrive into Ireland from a country not on the green list.
It said the guidance does not state that a negative Covid-19 test shortens the 14-days requirement.
Mr Hogan's primary residence is in Brussels and he arrived in Ireland on 31 July, travelling to his temporary residence in Kildare.
'Made big mistakes'
In their joint statement, Taoiseach Micheál Martin, Tánaiste Leo Varadkar and Green Party leader Eamon Ryan said the guidelines "clearly required him to restrict his movements for 14 days".
They said he should also have limited his movements to and from Kildare for essential travel only, and he should not have attended the golf dinner.
The statement adds that people are "correctly angered by these actions".
They added that Mr Hogan was accountable to the European Commission and they awaited the outcome of the review being carried out by Ms von der Leyen.
Earlier on Tuesday, Mr Hogan told the Irish state broadcaster RTÉ that he broke no regulations while in Ireland, was no risk to anybody but made big mistakes and is very embarrassed.
Speaking to RTÉ News, he apologised once again for attending the Oireachtas Golf Society dinner.
Mr Hogan repeatedly argued that his negative test for Covid-19 exempted him from the requirement to restrict movements for 14 days.
It also emerged at the weekend that the commissioner was stopped by gardaí (Irish police) for using his mobile phone while driving in County Kildare on 17 August.
The county has been under strict restrictions that prevent people from travelling in and out except in exceptional circumstances.