Taoiseach Micheál Martin, Tánaiste Leo Vardakar and Transport Minister Eamon Ryan say "it is clear" Phil Hogan breached public health guidelines on his recent trip to Ireland.
The three party leaders say they acknowledge his recent account of his movements when he travelled here last month.
But they say that "concerns remain."
A joint statement says: "It is clear that breaches of public health guidelines were made by Commissioner Phil Hogan since he travelled to Ireland.
"The Government guidelines clearly required him to restrict his movements for 14 days.
"He should also have limited his movements to and from Kildare for essential travel only, and he should not have attended the Oireachtas Golf Society dinner.
"People are correctly angered by these actions given the sacrifices so many have made to adhere to public health guidance.
"In addition, his delayed and hesitant release of information has undermined public confidence."
But they add that Commissioner Hogan is accountable to the President of the European Commission, Ursula von der Leyen.
"The Government now awaits the outcome of the review being undertaken by the president.
"Ultimately the Commissioner is accountable to the EU Commission, not to the Irish Government or to the Oireachtas", the statement adds.