Round-table talks chaired by the Taoiseach Brian Cowen and the British Prime Minister Gordon Brown and involving the North's five mainly assembly parties took taking place at Hillsborough Castle.
The Northern Secretary, Shaun Woodward, said the plenary session, which lasted just over an hour, had been a very constructive exchange of views.
He said all the party leaders had spoken at the talks. Joined by the Minister for Foreign Affairs, Micheál Martin, Mr Woodward said the plenary provided a positive platform for the resumption of bilateral talks.
Mr Martin said Brian Cowen and Gordon Brown had noted that there was very significant common ground about the way forward.
Earlier, Sinn Féin negotiator Gerry Kelly said his party was there to finish the job and they were determined to see it through.
He said they wanted to get the issues sorted out.
He also said he believed if the political will was there on behalf of all the parties then he thought they could achieve a solution.
DUP leader DUP Peter Robinson said he was hopeful that a resolution could be reached at the talks, which are being held at Hillsborough Castle in Co Down.
SDLP leader Mark Durkan said no 'vanity veto' should be used by the political parties. 'Instead of having completion of justice, you potentially have a complete mess,' he said.
Brian Cowen and Gordon Brown had led negotiations with the Democratic Unionist Party and Sinn Féin into the early hours of this morning.
They had flown to Belfast yesterday evening after a last-ditch attempt to secure a compromise between Peter Robinson and the Sinn Féin Deputy First Minister Martin McGuinness failed.
Their intervention came amid fears republicans could collapse the fragile institutions - forcing a snap Assembly election - if the DUP does not agree to a swift transfer of policing and justice powers from Westminster.
The two leaders are understood to have cleared their diaries for the coming days in anticipation of intensive exchanges with the rival politicians.
Late last night the two governments held private meetings with DUP and Sinn Féin negotiating teams.
Senior figures from the Ulster Unionist Party, the SDLP and the Alliance Party also arrived at the talks venue to be briefed on progress.
Sinn Féin said they are still holding out for a firm devolution date.
DUP again insisted they require concessions on how Orange Order parades were managed before they give the go ahead for the transfer.
The largest unionist party did, however, indicate they would be open to proposals on how to resolve the thorny parades issue.
Sinn Féin minister Conor Murphy emerged from the talks insisting that his party was seeking a date for devolution of policing powers and wider agreements that would ensure a true spirit of partnership and equality between republicans and unionists at Stormont.
He said: 'We are here clearly to get a date for the transfer of powers on policing and justice. That has been our focus.
'We want to see an agreement here. We want to see the institutions working properly.
'But they can only work properly if we have partners in these institutions who are willing to work them.'
His party claimed that within three months of the 2006 St Andrews Agreement that paved the way for the power-sharing government, Sinn Féin had fulfilled its obligations by backing the PSNI.
He said that three years on, the DUP had yet to fulfil its commitment to allow political responsibility for law and order to be brought within the Assembly.
Minister for Foreign Affairs Micheál Martin said the governments were committed to finding an agreed way forward.
