PSNI claims that the IRA is still in existence have been rubbished by Sinn Féin president Gerry Adams.
Mr Adams strongly denied the claims – saying: “The IRA is gone and not coming back.”
The Police Service of Northern Ireland's discussion on the existence of the IRA was triggered by the recent murders of Kevin McGuigan and Gerard ‘Jock’ Davison, both former members of the IRA.
Mr McGuigan was shot several times at point-blank range outside his home on August 12, while Mr Davison was killed in May in similar circumstances.
A senior PSNI officer last week drew a link between Mr McGuigan's killing and the IRA - but the PSNI confirmed in its statement that there was no evidence to suggest this is the case.
On the back of Mr McGuigan’s murder almost two weeks ago, Mr Hamilton said: “At this stage we assess that some Provisional IRA organisational infrastructure continues to exist but has undergone significant change since the signing of the Belfast Agreement in 1998.”
He went on to say that the PSNI does not believe the organisation exists for “paramilitary purposes”.
But Mr Adams hit back at these claims and denied that the organisation still exists.
“The war is over,” Mr Adams said. “There is now a peaceful and democratic path to achieve republican objectives.”
“Those individuals who do not embrace this and are pursuing their own agendas do not represent republicanism and should be held to account by the criminal justice system.”
The IRA declared an official end to its armed campaign 10 years ago on July 28, 2005.
The announcement came seven years after the signing of the Good Friday Agreement in 1998, which put an official end to the Troubles in the North of Ireland.
But there have been persistent claims since the ceasefire that some members of the organisation were still active.
While the PSNI acknowledged that the IRA had moved on from its campaign of violence for the most part, it was noted that: “Some current Provisional IRA and former members continue to engage in a range of criminal activity and occasional violence in the interest of personal gain or personal agendas.”
The Government in the Republic have been coy in their response to the fallout of the claims.
Minister for Foreign Affairs Charlie Flanagan evaded the issue by saying he hoped to speak directly to the North's Secretary of State Teresa Villiars on the matter soon.