The Tánaiste Leo Varadkar says he's confident he didn't breach COVID-19 guidelines by attending a function organised by former Minister Katherine Zappone.
However, both he and Simon Coveney have today acknowledged "mistakes were made" in the way the former minister was appointed as a special envoy.
Ms Zappone has told the Government she won't take the job, amid criticism of the appointment and her organising of an event for 50 people at the Merrion Hotel last month.
Mr Varadkar was among those who attended the outdoor event on July 21st.
In a statement this evening, the Tánaiste said he attended for around 45 minutes - saying he 'confirmed in advance' with Ms Zappone that the event was in line with COVID regulations.
He said: "Government regulations permit organised outdoor gatherings and events of up to 200 people. There were about 50 people present.
"The definition in the regulations includes social events as well as recreational, exercise, cultural, entertainment or community events. I am confident these regulations were not breached. This matter has been checked with the Attorney General.
"I accept that mistakes were made in the manner in which Dr Zappone was appointed a special envoy and regret the controversy it’s caused."
The Government has said there will be "further updates" to the guidelines to give clarity about how future outdoor events may operate.
Foreign Affairs Minister Simon Coveney, meanwhile, also acknowledged that "mistakes were made" in how the appointment was brought to Government.
He pledged that "lessons will be learnt".
He added that he understands Ms Zappone's decision, and thanked her "for being willing to work on Ireland's human rights priorities".
The latest developments come after opposition parties and a government senator sharply criticised both the appointment process and the holding of the event in Dublin.
The Merrion Hotel has insisted it has adhered to COVID regulations at all times.
Meanwhile, the Attorney General has advised the Government outdoor events for up to 200 people are allowed for social reasons - as long as they're not weddings, sporting events, training or in a private home.
In a statement this evening, the Government said: "The Government has been advised by the Attorney General that regulations provide for organised outdoor events and gatherings up to 200 people, including social, recreational, exercise, cultural, entertainment or community events.
"Further updates will be made to the guidelines to ensure that people have clarity about how organised outdoor events may operate into the future."
The Government's website currently states that organised outdoor events of up to 200 people are allowed "in the majority of venues".