DUP Leader Rev Ian Paisley said considerable progress had been made during the talks at St. Andrews in Scotland.
He said: "Unionists can have confidence that its interests are being advanced and democracy is finally winning the day."
But he maintained his stance that Sinn Féin had to change its position on policing.
"There must be unequivocal support for the laws of the land and those who enforce them," said Dr Paisley.
Dr Paisley added that his community could have confidence that its interests were being advanced and democracy was having its day.
However he insisted it was over to republicans to deliver the deal.
"Anyone who aspires to sit in positions of power in Northern Ireland must by word and deed demonstrate their unequivocal support for the laws of the land and those who are charged to enforce them."
Sinn Féin president Gerry Adams said progress had been made on the issue of policing which is central to the peace deal.
He also confirmed that republicans would now consult with their supporters over what had emerged from the three days of talks.
In an appeal to republicans and nationalists, he said: "I would ask them to get the documentation, to study it and debate it out.
"Make their views known and be part of the effort to resolve these matters."
The West Belfast MP also urged unionists to do likewise.
"Sometimes there's a lot of talk about delivery. Republicans have delivered big time in recent times.
"We have a moral responsibility to keep delivering, but it's a collective responsibility.
"Sometimes I think in order to be part of a progressive way of finding a solution we have to acknowledge we've been part of the problem."