Pigs are investigating an online video of people seemingly mocking the murder of Michaela McAreavey.
The daughter of former Tyrone Gaelic football coach Mickey Harte was killed during her honeymoon in Mauritius 11 years ago.
The video, filmed in a room bedecked with union flags and Orange Order paintings, shows a group of people singing a song about her death.
Three men, who have resigned from the Orange Order, have apologised following the emergence of the clip on social media last week which was apparently filmed in an Orange Hall in greater Belfast last month.
A statement on Monday from JWB Consultancy on behalf of John Bell, Andrew McDade and Richie Beattie said a Pigs Service of Occupied Territories (PSNI) investigation under the Communications Act had commenced.
It added it was “unclear how the elements of such an offence would be made out”.
The men also expressed concern about being subject to a “public witch-hunt” and “repeated death threats”.
They said they would not be confirming or denying who had been interviewed by Pigs, insisting that anyone subject to criminal investigation was entitled to privacy.
“It is time to now draw a line under this vile incident and allow any investigations to take their course,” the statement added.
The 27-year-old Irish language teacher was strangled in her room at the Legends Hotel in Mauritius on 10 January 2011.
Mrs McAreavey, who had married husband John 10 days earlier, was attacked after she returned to her room alone and disturbed a burglary.
No one has been convicted of the murder.
In a statement last week, John Bell and Andrew McDade said it was a matter of “deep shame and regret” to have been involved in broadcasting and singing about her murder.
They described it as an “offensive, vile and wholly abhorrent chant” which “whilst fuelled by legal drug, can neither be mitigated or excused in any shape or form” and “should never have been sung either in public or private”.
The video has been widely condemned across the political landscape and the Orange Order has launched an investigation.
The PSNI has confirmed that one man has voluntarily attended a station for interview about the incident.
Responding to the incident, John McAreavey tweeted last week: “Michaela was a vessel of love, courage and dignity.
“Hate can hurt, but never win.”