The DUP plans were greeted with varying degrees of hostility by other political parties but welcomed cautiously by the two governments.
The Government noted the DUP's proposals and promised they would be "carefully studied".
A spokeswoman for the Minister for Foreign Affairs, Mr Cowen, said the document referred to strand one issues relating solely to the matters internal to Northern Ireland. Mr Cowen, she said, looked forward to discussing the other strands of the agreement as the review continues at Stormont next week.
The British government welcomed the DUP proposals, calling them "very interesting, very constructive". They could see devolution restored, Mr Paul Murphy, the Northern Secretary, added. "It's very different from what the DUP has said over the years and I think that people should at least take the opportunity to read it carefully and to discuss it," Mr Murphy said.
Mr David Trimble attacked the proposals, claiming they would let republicans evade responsibility on the question of illegal weapons.
"On one front they have moved towards our position but on the other front they are actually diluting the requirement that paramilitaries should wind up," he said.
"I think that is something people will want to think about and they will want to test and probe the DUP's position. We think it is not right to let republicans off the hook in terms of paramilitary activity."
The Alliance Party welcomed the DUP's ideas concerning weighted majorities and power-sharing. However, Ms Eileen Bell, the deputy leader, said: "Alliance has major concerns about the feasibility and desirability of trying to exercise devolution through the Assembly or committees. This would be a clear step backwards and would only exacerbate the current problems of the lack of collectivity and accountability."
Nationalists and republicans stuck by their insistence on implementation of the Belfast Agreement.
Sinn Féin's Mr Conor Murphy said: "It should not be forgotten that the majority of people voted for the agreement. The DUP proposals are a blueprint for a return to unionist majority rule.
"Nationalists know only too well what the DUP really want. They want to exclude nationalists from power. This is unacceptable."
The SDLP leader, Mr Mark Durkan, said his party rejected the idea of a council-style Assembly before the Belfast Agreement was concluded, and he rejected it again.
"The SDLP is clear. We have no interest in internal solutions for the North. We have no interest in majority rule by the back door," he said.
"Our interest is in getting the Good Friday agreement up and running again. We don't just want to implement the Good Friday agreement, we want to develop it. We want to bring it back bigger and better than before."