Representatives from Sinn Féin and the Democratic Unionist Party are to meet British prime minister Gordon Brown in Downing Street today.
First Minister Peter Robinson and Deputy First Minister Martin McGuinness want to discuss concerns over issues including policing and justice, education reform and an Irish Language Act.
It is understood however that it will be the North's parties that will take the lead in today's discussions, with Brown and the Irish Government playing the role of facilitators.
Democratic Unionist Party (DUP) leader Mr Robinson succeeded Ian Paisley as First Minister yesterday after negotiations avoided a potential crisis in the power-sharing administration.
Sinn Féin had been considering not re-nominating Mr McGuinness amid unhappiness over the failure to devolve security powers to a minister in the North, plus the DUP blocking of republican initiatives.
The DUP believes there is not adequate community confidence to allow the transfer of policing and justice powers at this stage, but the parties have agreed to give urgent attention to the outstanding issues.
Both have differing interpretations of the 2006 St Andrews Agreement which paved the way for restored power-sharing in May 2007.
It is believed today's discussions, which are expected to begin around 10am and to last several hours, will highlight the progress made so far in the North.
While Sinn Féin sources see the talks as a chance to focus minds on the need for agreement on controversial issues, the DUP has said today represents a continuation of the engagement between the parties that has gone on for a number of months.
It is possible a further meeting may be scheduled to review progress, but the discussions are not being seen as a repeat of the hot-house negotiations that featured prominently over the last decade.
Mr Brown has said urgent issues to be discussed included the forward investment strategy, the economic situation, policing and justice and concerns over paramilitary organisations.
Dissident republicans opposed to the peace process have tried to kill policemen in recent months and the loyalist Ulster Volunteer Force (UVF) is under pressure to destroy weapons.
The DUP also wants to see the removal of existing paramilitary structures, including seeing the IRA's ruling Army Council stand down.
Contentious Orange Order parades, the Irish language and education will also be discussed.
Unresolved marches include that opposed by nationalist residents at Drumcree in Portadown, Co Armagh.
DUP culture minister Edwin Poots has not progressed an Irish Language Act while his party is opposed to Sinn Féin's plans to scrap academic selection for schoolchildren.