But ahead of the second anniversary of the trial of two men accused of the killing, they said they are “increasingly frustrated” with the slow progress of criminal proceedings.
In their statement the family also hit out at what they see as a lack of help from the Mauritius authorities.
It said: “As the second anniversary approaches of the trial of those accused of Michaela’s murder, the families are more determined than ever that justice will be done.
“They are hoping a settlement can soon be reached with the hotel in respect of the civil proceedings but they are growing increasingly frustrated by the slow progress of the criminal proceedings.
“In particular, they have been disappointed by the reluctance of the Mauritian authorities to keep them updated with developments.
“It was promised by the Mauritian Prime Minister that justice would be done and would be seen to be done in this case.
“However, as time marches on and the criminal proceedings seem to have ground to a halt, this promise is ringing hollow.”
Michaela was killed during an apparent botched robbery as she honeymooned with husband John McAreavey at the then Legends Hotel on the island in January 2011.
Two of the hotel’s staff, Sandip Moneea and Avinash Treebhoowoon, were acquitted of her murder in July 2012 and there have been claims local police botched the investigation.
Civil proceedings have also been launched against the hotel by the 27-year-old teacher's family.
Her father, Tyrone GAA boss Mickey Harte, and John have spoken movingly since her death about how their faith has helped them cope with the loss.
John has started a new relationship since the tragedy and has received the blessing of Mr Harte.
Thousands of mourners attended Michaela’s funeral near her family home in Ballygawley, Co Tyrone. She had married John just 12 days before her murder and was buried in her wedding dress.
The McAreaveys were celebrating their marriage at the Legends Hotel when John found his bride dead in the bathtub of their room.
Michaela had left a poolside restaurant to get biscuits from the room.
When she didn’t return John went to the room and found her body. She had been strangled.
Police said she was killed after disturbing thieves in her room.
Five hotel workers were arrested over the murder before two were charged but cleared during a marathon trial at the island’s Supreme Court.
No one responded to attempts to get a comment from the Mauritian Embassy in London at 03.06.2014.