Published Monday, 12 November 2012
In a statement to the Irish News newspaper, the group says the killing was linked to conditions at Maghaberry Prison where republican prisoners are refusing to wash in an attempt to secure political status.
There has been a long running republican protest at the jail in relation to strip-searching and the treatment of dissident prisoners.
The 52-year-old father of two was shot by gunmen on the M1 near Lurgan, Co Armagh on Thursday 1 November as he drove to work.
Mr Black, who was from Cookstown, was laid to rest last Tuesday. During his service, mourners heard that he was "a man committed to peace."
In July, it emerged that some of the main dissident republican terrorist factions in Northern Ireland were uniting to form a new version of the IRA.
Security correspondent Brian Rowan told UTV that "there are no secrets and no mysteries about this group."
It's a coalition of a number of dissidents who were out there - The Real IRA, Republican Action Against Drugs and a number of unaffiliated dissidents who have come together now to call themselves the IRA.
"The MI5 and police have been looking at elements within that IRA coalition as the likely people behind this gun attack on David Black," he continued.
"And [it's] no surprise either about what the backdrop to the shooting was - and that's the prisons row and protest within Maghaberry jail."
Mr Rowan added that it needed to be made clear this new grouping was not capable of "recreating, rerunning or reconstructing" what was the past IRA campaign.
"This organisation will pop its head up now and again. It has the deadly capacity to kill - but it hasn't got the capacity to sustain a long campaign."
Paul Givan, the DUP's justice spokesman, said that it is clear that there are "some within Northern Ireland who wish to drag the entire community backwards."
"The precise nature of whatever group has claimed responsibility for Mr Black's murder does not change the brutal nature of this crime."
He continued: "It should also have no impact upon the efforts made to ensure that those responsible are swiftly brought to justice.
"The murder of Mr Black cannot be justified and neither could any of the murders of the other 29 Prison Officers who were murdered because of the uniform they wore.
"The reality remains that those who murdered Mr Black come from within a community and someone will have been aware of their activities and their movements.
"It is vital that anyone with information about these people helps to put a stop to these terrorists and allows justice to be served."
Gerry Kelly, Sinn Féin's policing spokesperson, insisted: "This is not the new IRA. There's a number of organisations that call themselves the new IRA
"There is only one IRA - it fought a war with the British. There have been negotiations, we have a Good Friday Agreement," the north Belfast MLA added.
"We have had a democratic mandate [from] after 1998 which says everybody wants to move on."
© UTV News