Speaking afterwards, the DUP's Edwin Poots said the mood in the discussions with Sinn Féin had been positive and said they had achieved greater clarity about what needed to be done to secure a deal.
Mr Poots said the mood of the discussions was more up than down.
The talks have been adjourned for tomorrow and will resume on Monday.
A deadline imposed by Taoiseach Brian Cowen and British Prime Minister Gordon Brown to reach a settlement passed yesterday lunchtime.
The parties were told that a failure to secure a deal by then would see the two governments publish their own proposals to end the impasse over transferring law and order powers.
However, with meaningful engagement between the DUP and Sinn Féin continuing through yesterday the timeframe was allowed to slip as Dublin and London continued to monitor progress.
Minister for Justice Dermot Ahern has said the British and Irish governments are reluctant to publish their proposals to break the latest deadlock 'as long as there is a glimmer of hope' Sinn Féin and the DUP can reach agreement.
Speaking on RTÉ Radio One's Saturday View, he said it is far more preferable if the parties can reach agreement on the issues themselves and he believes both sides want a deal.
Sinn Féin want a swift devolution of policing and justice powers from Westminster to the Stormont Assembly, while unionists want new arrangements for overseeing loyal order parades before giving the go ahead.
Mr Poots said last night: 'There has been a considerable amount of work done. I think we are getting to know where the bottom lines are here, and I think it is absolutely necessary that we have total clarity and certainty both on policing and justice, and on the parades issue.'
But he said he wanted an unambiguous deal that 'every Ulster man and woman' could understand.
He added: 'There can be a deal but it can only be on the basis of respect and equality. Some people think they can ride roughshod over the DUP, that they are going to bully them and bully the unionist people...that's not going to happen.'
Sinn Féin's Conor Murphy, asked if 'a deal was on', said: 'Not as yet, it's not on.
'I hope that that changes over the coming hours, and we will certainly remain focused to try to achieve that, but unfortunately to date, a deal is not yet on.'
Mr Murphy added: 'If there is a possibility of a deal, we will pursue that, but at some stage we will have to call whether the DUP are capable or willing to do the business or not.'
Mr Cowen and Mr Brown opened the talks on Monday, but failed to secure a deal before leaving the venue on Wednesday.
Negotiations continued, but speculation earlier yesterday that the two leaders could return to Hillsborough to seal a successful conclusion to the talks dwindled as the talking went on without a final deal.
Mr Cowen and Mr Brown want the two sides to agree a process to transfer the powers from London to Belfast by the start of May.
The key sticking point is DUP demands for the abolition of the Parades Commission, which adjudicates on contentious marches, and instead leave it to an independent panel, appointed by the office of the First and Deputy First Minister, to arbitrate.
But they have also insisted they are also open to alternative proposals on parades.
New disclosures of more secret talks between Mr Robinson's DUP and Reg Empey's Ulster Unionist Party, under the auspices of the Orange Order, in an attempt to agree a unionist unity electoral pact are unlikely to help the already tense atmosphere around the negotiating table, and the signs going into today's discussions offered little hope of a breakthrough.
The parades issue clearly remains the major obstacle and if there is no deal, then there is a distinct possibility Sinn Féin will walk away, collapsing the power-sharing executive and triggering new Stormont elections.
SDLP leader Mark Durkan called on politicians involved in the Hillsborough talks to step up and complete devolution of policing and justice.
'We are now on the threshold of a very big choice - we can go for complete devolution or a complete mess,' he said.
The negotiations are being supervised by Northern Ireland Secretary Shaun Woodward and Minister for Foreign Affairs Micheal Martin.
The DUP leader, Peter Robinson, will be attending today's negotiations for only a few hours.
It is likely that discussions will adjourn in the late afternoon and that early next week there will be a push to conclude the talks successfully.
The current set of talks is the longest running negotiations in the history of Northern Ireland's peace process.
