Labour Party leader Alan Kelly has said the head of the European Commission should seek Phil Hogan’s resignation.
Taoiseach Micheal Martin and Tanaiste Leo Varadkar have also asked the EU trade commissioner to consider his position, following his attendance at the Connemara golf dinner.
The Dail is to be recalled early to discuss the fallout from the event.
The Irish Hotels Federation (IHF) has said it had no role in organising or providing clearance for last week’s Oireachtas Golf Society dinner in Clifden, Co Galway.
Mr Kelly said: “It is incumbent on Taoiseach Micheal Martin and Tanaiste Leo Varadkar to now inform the president of the European Commission Ursula von der Leyen that they no longer have confidence in the Irish commissioner Phil Hogan and that she should ask for his resignation pursuant to Article 17 of the Treaty on European Union.”
The Taoiseach has said public figures who attended the event, with more than 80 people across two rooms present, committed a “monumental” error of judgment.
A statement from the Government said: “The Taoiseach, Tanaiste, and minister Eamon Ryan have agreed that the Dail should be recalled following the reopening of schools.
“The Taoiseach will make this request to the ceann comhairle on Monday.”
The Dail had not been due to return until September 15.
Mr Martin said his former agriculture minister, Dara Calleary, had done the right thing in resigning after he attended the dinner, amid a public backlash at the event being held during the pandemic.
Supreme Court judge Seamus Woulfe was also in attendance.
Gardai are investigating whether the dinner at the Station House Hotel in Clifden on Wednesday night had breached coronavirus regulations.
The Government said on Tuesday it was reducing the number of people allowed to gather in a bid to reduce the rate of spread of coronavirus.
Tables in restaurants should not exceed six people, from no more than three households, and no more than 50 people should gather indoors.
An IHF statement said: “The IHF provides general guidance and at all times we encourage hotels and guesthouses to comply with the required guidelines.
“We do not have any role in enforcing, monitoring or approving the implementation of this guidance or operational guidelines.”
On Wednesday morning, the IHF received a follow-up query from the organiser of the Oireachtas Golf Society in relation to the guidelines for indoor gatherings.
Last night I attended a function I committed to a number of weeks ago, to pay tribute to a person I respected and admired greatly. In light of the updated public health guidance this week I should not have attended the event. I wish to apologise unreservedly to everyone 1/2— Dara Calleary (@daracalleary) August 20, 2020
It indicated it had no update from the Department of Tourism on the guidelines.
The representative organisation added: “Existing guidance at that time still allowed for indoor gatherings of a maximum of 50 people at any one time.
“Multiple gatherings were allowed in venue facilities, provided they were in separate defined spaces and there were systems to prevent intermingling in common spaces.”
The Taoiseach denied his leadership had been damaged by the episode, but acknowledged public anger compromised his Government’s messaging around the pandemic.
Mr Calleary and Jerry Buttimer, deputy chairman of the Irish Seanad, announced their resignations on Friday.
The ceann comhairle of the Oireachtas has suggested the golf society be wound up.