Irish Foreign Minister Micheal Martin and Secretary of State for Northern Ireland Shaun Woodward
Talks aimed at resolving the impasse over devolution in Northern Ireland have made "considerable progress", the UK government has said.
But Northern Ireland Secretary Shaun Woodward said there was still "work to be done".
The DUP's Edwin Poots said there had been "considerable advancement", while Sinn Fein's Conor Murphy said his party remained "optimistic".
The talks at Hillsborough Castle, outside Belfast, will resume on Monday.
Sinn Fein and the DUP have been arguing for months over the timing and circumstances of the transfer of policing and justice powers to Belfast.
BBC NI reporter Yvette Shapiro said the gap between the two parties is believed to be getting smaller with the talks focusing on the "fine details".
Sinn Fein wants the powers transferred immediately, while the DUP has said that can only happen when there is "community confidence" among unionists.
The largest unionist party said that confidence could be built through a deal on how to resolve the parading issue. However, republicans have maintained that devolution should not depend on agreement on parading.
'Very long days'
The talks began on Monday when the British and Irish PMs went to Belfast.
The quality of the engagement by all of the parties has been the key determining factor
Irish Foreign Minister Micheal Martin
On Wednesday, Gordon Brown and Brian Cowen said that if there was no deal within 48 hours, they would publish their own proposals, but that deadline was allowed to pass with the parties still locked in discussions.
At about 2000 GMT on Saturday, the parties emerged from Hillsborough and Mr Woodward said all involved needed some time off.
"We have made, across what has now been six days, very long days, I think considerable progress," he said. "There remains more work to be done."
For Sinn Fein, Mr Murphy, was also upbeat: "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."
Speaking an hour earlier, Mr Poots said his party also wanted to "conclude the business".
"We are looking to tidy some things up tonight and there is some more work to be done on Monday," he said.
"We have been working towards creating certainty and clarity about the issues.
Sinn Fein's Martin McGuinness and Gerry Adams take a break from talks
"It's more important about getting the right deal, as opposed to a hurried deal."
'Not concerned'
The talks represent the longest period of sustained negotiations since the peace process began in the 1990s.
The negotiations are being led by Mr Woodward and Irish Foreign Minister Micheal Martin after the premiers left Northern Ireland on Wednesday.
Mr Martin said he was not concerned that the deadline for a settlement had been missed.
"Very experienced people have said to me deadlines have often been set with a purpose of being passed," he said.
"The quality of the engagement by all of the parties has been the key determining factor this week."
Nationalist SDLP Assembly member Alex Attwood said: "Our sense is that those negotiations continue to move forward steadily and in a positive fashion."
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