The parties have been on the brink of ending their powersharing government unless agreement on two issues, policing and justice oversight, and how Orange parades are managed, are resolved.
British Secretary of State Shaun Woodward confirmed the new optimism. "We have made, across six very long days, I think, considerable progress," he stated. Talks are due to resume again on Monday.
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.
Irish foreign affairs minister Michael Martin praised the parties. He said: "They are engaging in a way that is purposeful and with determination to resolve the issues.
After an exhausting six days members of both parties and both the British and Irish governments emerged late Saturday gave the thumbs up to an imminent settlement. They have been locked away in Hillsborough Castle outside Belfast.
Earlier last week the British and Irish Prime Ministers joined the talks but could not bring about a resolution. It is expected they may come back to Belfast on Monday to be on hand for the new agreement if it reached.