Northern Ireland's politicians are being called into talks next week to resolve the Stormont crisis.
David Cameron and Irish Taoiseach Enda Kenny ordered negotiations to break the deadlock at Stormont as security chiefs said they would support an independent assessment of paramilitary groups.
A Downing Street statement said devolved power-sharing is facing a real threat unless there is urgent progress.
"As a result of these discussions the Government has concluded that there is a clear need to convene urgent, intensive and focused cross party talks, involving the parties engaged in the negotiations that led to the Stormont House Agreement," the statement said.
"It is vital for the sustainability of the devolved institutions that all parties seize the opportunity for urgent talks to address these issues."
Mr Kenny said: "We envisage that this process of talks should be short, focused and intensive and deal with full implementation of the Stormont House Agreement as well as the trust and confidence issues arising from the legacy of paramilitarism.
"If the sustainability of the devolved institutions is to be ensured, it is absolutely critical that these talks are advanced with a sense of urgency and that all of the parties constructively seize this opportunity."
Mr Kenny and Mr Cameron spoke on the phone yesterday and agreed the initiative.
The talks are planned for next week at Stormont House with Secretary of State Theresa Villiers representing London and Foreign Affairs Minister Charlie Flanagan, Dublin.
"The purpose of the talks is to secure full implementation of the Agreement and to deal with issues arising from the impact of continued paramilitary activity in Northern Ireland," Downing Street said.
The move came after the Police Service of Northern Ireland (PSNI) offered a new assessment of Provisional IRA activity stating that aspects of the terror organisation have gone away, its active service units do not exist any more and what remains fulfils a radically different purpose than during the Troubles.
Both the Irish Government and the Democratic Unionists support a new form of paramilitary monitoring of the ceasefires.
The breakdown in relations at Stormont reached a new low after the killing of a former IRA father-of-nine Kevin McGuigan, allegedly by former terror associates.
That murder earlier this summer caused political uproar after PSNI Chief Constable George Hamilton said the IRA - which was supposed to have gone away a decade ago - still exists for peaceful purposes and the shooting was carried out by individual PIRA members but not sanctioned at a senior level.
The police chief said: "The monitoring of paramilitary groups as conducted, for example, by the Independent Monitoring Commission (IMC) until 2011, was part of a political agreement.
"The police service would be supportive of any political intervention to create some form of independent assessment process in the future."
The IMC was established by the British and Irish Governments to monitor the ceasefires of paramilitary groups after the 1998 Good Friday Agreement, which ended decades of violence.
Mr Hamilton said it would be a political decision whether to set up another body like the IMC.
He added: "We don't actually have a statutory responsibility to monitor and report to political parties on the status of paramilitary groups.
"If there is a decision taken politically that there would be some sort of monitoring commission introduced clearly it would fill that gap."
Mr Hamilton said any monitoring should include loyalist groups like the Ulster Volunteer Force and Ulster Defence Association.
Senior police briefed politicians and independent members of the Policing Board about the Provisional IRA today in Belfast.
Assistant chief constable Will Kerr said: "At the operational tier, active service units, we don't believe that tier exists any more. A senior tier exists for a radically different purpose than 20 years ago."
He said there was no terrorist command and the IRA was not engaged in terrorism.
"It is involved in pursuing an exclusively peaceful, political agenda."
Police believe the killing of Mr McGuigan was a revenge attack by republican associates of IRA commander Gerard "Jock" Davison, who was gunned down in Belfast in May.
The Ulster Unionist Party (UUP) last week said it could no longer work with Sinn Fein because trust has been shattered and has left the power-sharing ministerial Executive at Stormont.
Northern Ireland's largest party, the DUP, has called for the Assembly to be suspended for four weeks to allow for intensive talks.
Sinn Fein has said the IRA has gone away but supported calls for discussions.
Northern Ireland Secretary Theresa Villiers said the fallout from recent murders in Belfast highlighted the need to see all paramilitary organisations disband.
"The Prime Minister and I, along with the Irish Government, agree that there is a need for urgent, focused and intensive talks.
"A failure to resolve the issues under discussion would raise serious questions about the sustainability of the devolved institutions.
"I would expect each of the parties to give these talks their highest priority as we seek to find a way forward - to implement in full the Stormont House Agreement and to look at ways of dealing with the scourge of paramilitarism, from wherever it might come."