Talks ended on Saturday night without agreement but hopes were mounting that a deal could be struck when negotiations resume on Monday.

Northern Ireland Secretary Shaun Woodward said: "We have made, across six very long days I think, considerable progress. There remains work to be done."

Taoiseach Brian Cowen and British Prime Minister Gordon Brown launched the dialogue at Hillsborough Castle, Co Down, on Monday.

Sinn Fein and the Democratic Unionists disagreed over a solution for dealing with loyalist order parades.

The governments threatened to publish their own proposals to break the deadlock.

Foreign Affairs Minister Micheal Martin praised the parties. "They are engaging, in our view, in a way that is purposeful and with determination to resolve the issues."

Sinn Fein negotiator 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 that point now where negotiations will end."

Democratic Unionist 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."

If there was no deal there was a possibility Sinn Fein would walk away, collapsing the powersharing executive and triggering new Stormont elections.