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Mr Orde also confirmed that his detectives know the identities of the gang members suspected of stabbing the father of two to death, but their investigation is being thwarted by witnesses refusing to give evidence.
The attack on Mr McCartney and his friend Brendan Devine has put the IRA under the kind of pressure that it has rarely endured since the days of the Peace People campaign of the mid-1970s.
Yesterday's statement was apparently intended to show the IRA's commitment to ensure Mr McCartney's killers are brought to justice, but was instead condemned as exposing the group's continuing willingness to use violence.
Mr Orde appealed for the community to abide by the rule of law and for witnesses to come forward to allow the police to formally press charges.
"People sending names to each other rather like naughty school children does not help this investigation. We need those 70 people to have the confidence to speak to us," he said.
"We are very clear who our suspects are. What we need is for the witnesses - the 70 people in the bar who apparently witnessed Robert McCartney's murder - we need those people to have the confidence to come and speak to us.
Martin McGuinness, Sinn Fein's chief negotiator, told Today that he also wanted witnesses to come forward but stopped short of saying they should contact police directly, instead suggesting information is passed through a third party such as solicitors or the police ombudsman.
He said: "We have to recognise that out of this present terrible situation a very strong effort is being made to encourage people to come forward so we can have the best possible, that those responsible for the murder of Robert McCartney appear in a criminal court. We want people to stand up in court and put these people behind bars."
The IRA statement came 11 days after the group announced that it had expelled three members - two of them high-ranking - for involvement in the murder. The Sinn Fein president, Gerry Adams, has also said that he passed seven names of implicated republicans - some of whom he said he knew - to the Northern Ireland police ombudsman.
In chilling language the statement said: "One man was responsible for providing the knife that was used in the stabbing of Robert McCartney and Brendan Devine in Market Street. He got the knife from the kitchen of Magennis's Bar. Another man stabbed Robert McCartney and Brendan Devine. A third man kicked and beat Robert McCartney after he had been stabbed in Market Street. A fourth man hit a friend of Robert McCartney and Brendan Devine across the face with a steel bar in Market Street.
"The man who provided the knife also retrieved it from the scene and destroyed it. The same man also took the CCTV tape from the bar, after threatening a member of staff and later destroyed it.
He also burnt clothes after the attack."
The IRA's statement said that the organisation's conclusions were based upon "voluntary admissions" and urged "any witnesses who can assist in any way to come forward. That remains our position. The only interest the IRA has in this case is to see truth and justice achieved."
It added that Mr McCartney's family had made it clear that they wanted trials and not "physical action taken against those involved".
Ian Paisley, the leader of the Democratic Unionist Party, said the offer to shoot those responsible for the murder of Mr McCartney confirmed again that "terrorism is the only stock and trade of Sinn Fein/IRA". He said: "If anyone else had done this other than the IRA the police would have moved in to arrest them as a breach of the law."
But Gerry Kelly, a former IRA bomber and prison escaper who is now an elected Sinn Fein representative, said: "The shooting did not take place and it would not have been acceptable. Whatever people think of the IRA they have their own disciplinary codes or whatever, and in this case they stated it to the family and then did not act upon it. Now that is a changed situation in itself."
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