Taoiseach Enda Kenny has said he is "absolutely heartbroken" for the family of Michaela McAreavey and "the devastation" the result of the trial has had on her husband John.
Mr Kenny said "a beautiful Irish woman has been murdered" and on behalf of the people "I want to empathise with the grief of her family".
He said that the Mauritian authorities had stressed that justice would be done in this case but "clearly it hasn't been done".
Mr Kenny said governments did not interfere in the legal processes of other countries, but that the "outcome had been wholly unsatisfactory".
Earlier, one of the defence lawyers in the murder trial said he will meet Avinash Treebhoowoon today to discuss a possible claim for damages against the Mauritian state.
A jury at the island's supreme court yesterday acquitted the 32-year-old and his co-worker Sandip Moneea of the murder of the 27-year-old school teacher at the Legends Hotel in January of last year.
Speaking on RTÉ's Morning Ireland, defence lawyer Sanjeev Teeluckdharry said the past 18 months have been an ordeal for his client.
Mr Teeluckdharry said it will be difficult for Mr Treebhoowoon to return to normal life.
He said that he is very sad for Mrs McAreavey's family, but he blamed police incompetence for not finding the real culprit.
Mr Teeluckdharry said the reputation of the country had been damaged, not by the way justice was carried out, but by the incompetence of the police investigation.
He said he did not regret the line of questioning to John McAreavey during the trial. He said questions had to asked and everything had to be put in front of the jury.
Mr Teeluckdharry added: "I hope that the inquiry is re-opened and the matter is investigated in a proper form, a scientific and serious manner so that we can find justice."
Mr McAreavey is expected to return to Ireland this weekend with his father, sister and brother-in-law, Mark Harte.
The McAreavey and Harte families have said they will not be making any further comment on the trial.
A statement released on their behalf today said that they thanked people for their support and have asked the media to respect their right to privacy as they return home.