Independent Senator Gerard Craughwell has written to Garda Commissioner Drew Harris seeking an investigation into the celebratory gathering at the Department of Foreign Affairs, after Ireland secured a UN Security Council seat.
The controversy stems from a June 2020 gathering where officials had drinks to celebrate Ireland's successful United Nations campaign.
At the time, people were only allowed to meet with up to six people from outside their household.
Former secretary general Niall Burgess tweeted a photo of the event but it was quickly deleted.
Senator Craughwell said "either a law has been broken or it hasn't" and he argued that what he termed a "cosy internal investigation" by Iveagh House was not the way to examine the matter.
He added that he was "taken aback" that Foreign Affairs Minister Simon Coveney had not referred the matter to the Gardai or that the Commissioner hadn't instituted his own investigation.
Senator Craughwell said no-one could be above the law - particularly given 1,700 citizens have already faced fines for breaches of the Covid-19 regulations.
The letter, first reported in the Irish Independent, states: "There is massive public anger over this event".
The Senator said he was "unsure" if his request for a Garda investigation could be considered given the applicable regulations, which were subject to a six months statute of limitations, had now expired.
He said if it was the case that the Gardai had no sanction, then he couldn't see how any HR department in the Department of Foreign Affairs would be able to take disciplinary action either.
The Foreign Affairs Committee has decided to invite Minister Coveney to appear before it to answer questions about a controversial gathering in his Department.
Members met in private this afternoon and agreed to call Mr Coveney to address them after an internal report ordered by the Minister has been completed.
Secretary General Joe Hackett is compiling the investigation and it is due to be completed by the end of the month.
The Committee also agreed to write to Mr Coveney asking for the terms of reference, scope of the investigation and the timeframe for its completion.
It's understood that concerns will be expressed in the letter about the investigation being headed up by the Secretary General of the Department.
Mr Coveney has said those involved were "mortified" over the event and that the Department had apologised.
The committee is also likely to probe why the Foreign Affairs Minister did not reveal the existence of the investigation in an interview on Friday.
In addition, Tánaiste Leo Varadkar also did not appear to be aware of the inquiry when he spoke on Sunday.
A spokesperson for the Tánaiste has since said that Mr Varadkar was aware an investigation was under consideration but he did not know it had been decided.
Sinn Féin has accused Mr Coveney of blindsiding his colleagues by announcing the probe on Sunday evening.
Foreign Affairs spokesperson John Brady said the Minister had initially ruled out an investigation because he trusted his colleagues.
"This has come as yet another major distraction for the Minister and is very reminiscent of the Katherine Zappone scandal of last Summer."
With additional reporting by Sandra Hurley