Alliance Party leader David Ford has said that the Northern Ireland parties who met in a plenary session this afternoon were engaging constructively to discuss all the issues relating to the devolution of policing and justice powers to Stormont.
Mr Ford also said politicians meeting at Hillsborough Castle, near Belfast, could be working long into the night to try to break the deadlock before tomorrow's deadline.
Earlier, Acting First Minister Arlene Foster was briefed by her DUP colleagues.
The development came on the fourth day of negotiations to break the deadlock.
The Sinn Féin President, Gerry Adams, also briefed his party's officers.
If there is still no agreement by tomorrow, the Irish and British governments will publish their own plans to resolve the issues.
The outstanding issues remain the completion of the devolution of policing and justice powers and Orange Order parades.
Minister for Foreign Affairs Micheál Martin and Northern Secretary Shaun Woodward remained at Hillsborough overnight to oversee any discussions.
Meanwhile, the Orange Order has been at the centre of more behind-the-scenes moves to bring together the two main Unionist parties in Northern Ireland, it was revealed tonight.
Democratic Unionist Party leader Peter Robinson and Sir Reg Empey, head of the Ulster Unionist Party were involved in a meeting at the headquarters of the institution in Belfast at the beginning of last month.
A spokesman for the Orange Order said 'It was a private meeting to discuss Unionist unity which is a long term aspiration of the Orange Order.'
The Order's Grand Master Robert Saulters and secretary Drew Nelson hosted the discussions which took place before Mr Robinson temporarily stood down as the Northern Ireland First Minister in the aftermath of the sex and money scandal involving his MP wife Iris.
Earlier, the leaders of Ireland's four main churches have urged the politicians to redouble their efforts in the talks.
Senior clerics offered their prayers and support in a joint statement from Cardinal Sean Brady, Church of Ireland Archbishop Alan Harper, Presbyterian Moderator Dr Stafford Carson and Methodist President Rev Donald Ker.
The men said they wished to put on record their 'admiration for the commitment of all parties engaged in the talks to resolve the issues surrounding the devolution of policing and justice powers to the Northern Ireland Assembly'.
They added: 'The people of Northern Ireland expect their representatives to ensure that agreement is reached.
'There is an overwhelming desire throughout Northern Ireland for continued political progress and for the peace process to be sustained.'
