Taoiseach Micheál Martin has said he was "shocked and dismayed" to learn of Sinn Féin TD Brian Stanley's tweet celebrating two historical IRA attacks on the British army, saying it was "deeply, deeply offensive".
Mr Martin added: "I think Sinn Féin should deal with this in terms of Brian Stanley's position and they need to atone for what happened on that day [in 1979]."
The Taoiseach contended that the remarks "... damages our ability to reach out and genuinely try and create trust in a shared endeavour in the future on this island. It doesn't help that at all."
He added: "The language in the tweet "... erodes trust, in terms of, are people really genuine within Sinn Féin about reconciliation, or is it always about victory?"
Meanwhile, the office of the Ceann Comhairle confirmed this evening that it has received a letter from Northern Ireland First Minister Arlene Foster regarding the weekend tweet by Mr Stanley.
The letter will now be considered.
In it, Mrs Foster said Brian Stanley's statement has caused enormous offence to both the victims of terrorism in Northern Ireland and wider society.
"Mr Stanley's comments fall well short of the behaviour expected of any democrat, let alone an elected TD who holds an important office in your Parliamentary system, as the Chairman of the Public Accounts Committee. I would ask that you consider whether such comments meet the standards required of members of Dáil Éireann. I look forward to your assessment of Mr Stanley's actions and what actions the Dáil feels appropriate to take in these circumstances," the letter states.
The Dáil's Public Accounts Committee is divided over whether its chair, Mr Stanley, should recuse himself over the tweet.
The vice-chair of PAC and Social Democrats co-leader Catherine Murphy said while Mr Stanley had apologised and deleted the tweet, this was not sufficient to resolve the matter.
She said she was appalled by the tweet, adding that it cannot be "business as usual" at the committee on Wednesday.
Fine Gael TD Jennifer Carroll MacNeill, who is also a member of the PAC, said Mr Stanley should recuse himself as committee chair, however that suggestion has been opposed by other PAC members.
Fianna Fáil's Marc MacSharry said while the comments were very inappropriate and insensitive, Mr Stanley was a good chairperson and should not resign.
While critical of the tweet, Labour's Sean Sherlock and Independent Verona Murphy also said he had apologised and should remain as PAC Chair.
Fine Gael's Alan Dillon said it was a personal choice for Mr Stanley, while Green TD Neasa Hourigan declined to comment.
Sinn Féin's housing spokesperson Eoin Ó Broin said the party will not be taking any further action regarding Mr Stanley over his tweet.
Speaking on RTÉ's News At One, he that the remarks were "wrong" and "wholly inappropriate" but said Mr Stanley "did the right thing" in apologising and deleting the tweet.
Asked if Mr Stanley should recuse himself as PAC chairperson, Mr Ó Broin said: "I don't believe he should."
Stormont Deputy First Minister Michelle O'Neill said Mr Stanley deleted his "inappropriate and insensitive" tweet.
"We all have a responsibility to commemorate in a responsible manner."
She said old battles should not be refought.
"Our mission is to bring all the people of this island together and not keep us apart."
She said next year should not be defined by rancour and division.
Earlier, Minister for Foreign Affairs Simon Coveney said Sinn Féin frequently speak about the need for legacy infrastructure to deal with the past in a sensitive way in Northern Ireland, yet a senior member comes out with this "bile" on social media.
He said the remarks by Mr Stanley, which were later deleted, is another case of the "mask slipping" and the Laois-Offaly TD should know better.
Mr Stanley has apologised for the "content of an inappropriate and insensitive tweet I sent yesterday (Saturday)."
A Sinn Féin spokesperson said: "We note that Brian Stanley has deleted a tweet that was inappropriate and insensitive, and that he has apologised.
"We all have a responsibility in this Decade of Centenaries to remember and commemorate the past in a respectful manner."
Mr Stanley's tweet received more than 500 likes on the platform and was shared close to 400 times.
The Kilmichael ambush was an attack carried out by the IRA during the War of Independence in which 17 members of the Royal Irish Constabulary Auxiliary Division were killed.
The Warrenpoint ambush took place during the Troubles and saw 18 British soldiers killed by the IRA near Warrenpoint in 1979.
I wish Stanley was there to witness what I saw - former British soldier
One of the first soldiers on the scene after the Warrenpoint ambush has spoken of the devastation he witnessed that day in 1979 and called on all sides to embrace the beautiful country of Ireland, North and South, and move on.
Graham Eve said that you can try to explain to people what happened that day but no one will really understand it.
Although he has not seen the Sinn Féin TD's tweet, he said he wished Mr Stanley had been there on the day and witnessed what he saw.
Mr Eve said, 41 years later, neither he nor another friend who was with him that day, would come out with such hatred.
Speaking on RTÉ's News at One, Mr Eve said he has children and grandchildren that he loves to bits and does not want them to see or experience what he has "because of bigots and because of the colours orange and green, because it's getting us nowhere".
He said he knew everyone who died extremely well and they had all joined the army at the same time.
Mr Eve said the explosion turned him from a young man into an experienced hardened soldier, so when it came to the Falklands war, they just got on with it because they had "already been blooded".
He said that he never forgets what happened but that does not mean he cannot get on with his life and he wished other people "could get on with theirs and grow up".
He said he took part in a BBC programme with an ex-IRA man and that before anything was recorded that they sat and talked and found out they had a lot in common.
Mr Eve said if that man was to call and ask him for a favour, he said, he would do it.