The leaders of the three coalition parties say "it is clear" Phil Hogan breached public health guidelines on his recent trip to Ireland.
An Taoiseach Micheál Martin, Tánaiste Leo Vardakar and Transport Minister Eamon Ryan say they acknowledge his recent account of his movements when he travelled here last month.
In a statement, they say they also acknowledge his written and public account of his movements, and welcome his apology.
But they say that "concerns remain."
The 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 European Commission President, Ursula von der Leyen.
"The Government now awaits the outcome of the review being undertaken by the [European Commission] President.
"Ultimately the Commissioner is accountable to the EU Commission, not to the Irish Government or to the Oireachtas", the statement adds.
Mr Hogan has said his travel to and from Kildare while it was in lockdown was to collect "essential work papers."
He also confirmed he was stopped by An Garda Síochána for using a mobile phone while driving during the same trip on August 17th.
However he also said he tested negative for COVID-19 and claimed that a negative test result "ends the self-restriction period", referencing a Citizens Information web page.
The Citizens Information Board has moved to clarify the issue, and says the web page refers to those who have been told they are a close contact of a confirmed case.