Expectations are rising of a deal between Sinn Fein and the DUP on devolving justice powers and thus saving the Stormont institutions.
Following six days of negotiations at Hillsborough Castle in Co Down chaired by the Irish and British governments, Sinn Féin's Conor Murphy said: "We are maybe getting somewhere now. We have progress made, we are hopeful that we can finish this fairly quickly."
"We are getting towards the point now where negotiations will end."
Minister for Foreign Affairs Micheal Martin agreed, saying of the political parties: "They are engaging, in our view, in a way that is purposeful and with determination to resolve the issues."
There is no confirmation yet that Taoiseach Brian Cowen and British prime minister Gordon Brown will return to Northern Ireland to seal a deal on devolving justice powers and other contentious issues including parading.
They arrived in Hillsborough last Monday to oversee the talks but left on Wednesday without an agreement. However they set a 48-hour deadline on ongoing talks and left Northern Secretary Shaun Woodward and Mr Martin in charge.
The two premiers also said they would publish their own proposals, which include a date for the transfer of justice powers - a key Sinn Fein demand, in the event that the local parties failed to conclude their own agreement.
The talks participants rested today with a view to returning tomorrow morning.
As they left the castle last night Mr Woodward said: "We have made, across six very long days I think, considerable progress. There remains work to be done."
Standing alongside Mr Martin he added: "We felt yesterday that significant progress was being made, therefore it was right in the place of those talks happening to allow them to continue their work today."
DUP minister Edwin Poots said: "There is considerable advancement, what I said previously was that there would have to be certainty and clarity and there would appear to be greater certainty and clarity than was the case when I was speaking on Thursday night."
SDLP Assembly member Alex Attwood said: "Our sense is that those negotiations continue to move forward steadily and in a positive fashion."