The formal review of the 1998 Good Friday Agreement resumed on Tuesday in Belfast with feelings mixed on its prospect for success.
In the absence of the British and Irish Prime Ministers, the British government is preparing a paper for the parties summarising the views expressed so far.
The talks will continue next week.
British Direct Ruler Paul Murphy and the Minister for arts, sport and tourism in the 26 Counties, John O’Donoghue, sid they were upbeat that a political deal was achievable, pointing to genuine constructive engagement between the parties.
At a press conference Mr Murphy said that the past two days had marked some of the most positive meetings yet in terms of the details discussed.
He said the parties would receive a “progress report” on Monday in order to focus on key issues and next Tuesday the governments would continue to discuss with the parties issues relating to North-South relations and relations between the islands.
He said the two premiers would be meeting in Brussels tomorrow and would decide whether their direct involvement with the parties would be useful before the summer break.
“I remain absolutely convinced that progress can be made if the will is there on all sides. For their part the two governments will continue to make every effort to facilitate an agreed way forward.
“Where there is the will I believe there can be progress.”
Mr Murphy pointed out that discussions had been taking place between the governments and the DUP and with Sinn Féin over the last number of weeks, and that those issues were also being dealt with.
“These are the issues in front of us which need to be resolved to produce the confidence that is necessary to restore the institutions,” he said.
“On the one hand there is im-portance from a republican and nationalist side that they have confidence that unionists will engage in an executive here in Stormont.
“And on the other hand, of course, we have the issue of continued paramilitary activity which has to be addressed.
“These issues have to be addressed and we have been talking during the election period, mainly at officials’ levels, be-tween the governments and those two parties.”
Sinn Féin Newry and Armagh assembly member Conor Murphy said there had been greater application over the past couple of days in terms of trying to deal with the issues comprehensively than in previous discussions and that this was encouraging.
“We want to see a comprehensive resolution of all of the outstanding issues facing us,” he said.
“From Sinn Féin’s point of view we are very much up for finding that resolution. We will know next week whether all of the parties and both governments are similarly up for resolution.”
Ulster Unionists, who remain outside the review process, have claimed that the DUP is planning a deal to restore the North’s political institutions by the Autumn.
But DUP leader Ian Paisley said his party delegation members had left the Secretary of State and Mr O’Donoghue in no doubt that they would not accept any fudge of democracy on any of the issues.
“The DUP position of no terrorists in government is unalterable,” Mr Paisley said.
“The British government and the government of the Irish Republic must get down to business. There are difficult issues to resolve and they must be faced.
“The days of the Belfast Agreement are over. It is time to move forward on a democratic bas- is that allows government in Northern Ireland and any relationship with the Republic to be fully accountable.
“Unlike the Ulster Unionist Party, the DUP will keep its word.
“That false prophet in the form of (Ulster Unionist) Michael McGimpsey can rave as much as he likes about a deal but the reality is that unlike his party the DUP will not be putting terrorists into any government.”