In a statement issued late last Friday, Dr Navin Ramgoolam said the government and people "understand and share the grief and agony" of the Harte and McAreavey families.
He was speaking after convening a meeting of senior police chiefs and prosecutors to discuss the high-profile case, the investigation and prosecution of which has shaken faith in the holiday island's law enforcement system.
The comments by the political leader came as Mauritius's director of public prosecutions, Satyajit Boolel, said yesterday that he trusted the police force and its elite crime team to carry out a second investigation into Michaela McAreavey's murder.
The failure of Mauritian authorities to find and bring Michaela's killers to account was laid bare last Thursday with the sensational acquittal of Avinash Treebhoowoon and Sandip Moneea, the two hotel workers who were accused of murdering her.
The details of Doctor Ramgoolam's statement came through just as Michaela's heartbroken husband, John, and the family members who have supported him throughout the harrowing eight-week trial arrived into Dublin Airport for the final leg of their return home to Co Down.
Looking tired and drawn from the 14-hour flight, Mr McAreavey emerged from the airport's VIP arrivals suite shortly after 11am and was met by a car.
Dr Ramgoolam's vow to continue the pursuit of the case came just hours after Taoiseach Enda Kenny said he was "absolutely heartbroken" for the Harte and McAreavey families.
Mr Kenny recalled a pledge by Dr Ramgoolam following the murder at the luxury Legends Hotel in January 10 last year that justice would be done and seen to be done.
He said that the Government "would reflect" on the case but added that it "can't interfere in the legal processes of other countries".
Clearly mindful of the Taoiseach's comments and of the feelings of Michaela's family, Dr Ramgoolam insisted last Friday night he would make good his pledge to find the culprits.
He said: "The government has taken note of the verdict delivered in the Michaela Harte murder case. The government and the people of Mauritius understand and continue to share the grief and agony of the Harte and McAreavey families. Government is considering all options concerning further action in this matter, with a view to bringing the perpetrators of this heinous crime to justice."
Dr Ramgoolam spent a half an hour reviewing the case with law enforcement officials including the island's police commissioner; the head of the Mauritius Major Crimes Investigation Team (MCIT) Yousoof Soopun, who gave evidence about the police's inquiry in court; the director of the National Security Service; and the director of public prosecutions.
The MCIT, in particular, has faced severe criticism for its handling of the case and for claims by defendant Mr Treebhoowoon that he was subjected to three days of beatings by officers before he confessed to strangling Michaela because she caught him and co-defendant Sandip Moneea stealing from her hotel room.
Mr Boolel said he had faith in a second investigation but noted that the double-jeopardy rule meant the two acquitted men could not be tried again unless new evidence emerged.
He had said he was satisfied with the investigation into the murder but that lessons would be learned after the acquittal.
In an interview on RTE's Marian Finucane Show, Mr Boolel said the fact that Michaela's body had been found in a bath of flowing water meant that potential forensic traces were either diluted or removed.
He said his first reaction to the verdict was that too much reliance had been placed on a confession that was not supported by forensics.
He said video recordings of the interviews would have dismissed a lot of doubt about that. He had since advised the police commissioner in Mauritius that all future confessions be video or audio-recorded, and that the state's forensic services should be strengthened.
Asked if there had been a rush by the Mauritian authorities to charge the two men, he said: "That is utter nonsense."
He said the authorities had ensured that priority was given to the case and that it was tried in a reasonable time.
Mr Boolel said the authorities had "ample evidence" to justify taking the case to trial, and the evidence gathered had convinced them that they had a high chance of conviction.
While both the prime minister and DPP of Mauritius expressed their determination to see Michaela McAreavey's killer brought to justice, her widowed husband's Mauritian lawyer, Dick Su Wa, told Newstalk radio there was "no hope" that this would happen.
"I am, of course, angry and frustrated. I was disappointed by the verdict. I accept it but it doesn't mean I am happy with it. I think it (the investigation) is over to be honest," he said.
Michaela's father, Tyrone manager Mickey Harte, was in Hyde Park yesterday guiding his team to victory in the All-Ireland senior football championship qualifiers.