The leader of the Ulster Unionist Party, Mr David Trimble, has said "the general shape of the outcome of the current talks process" should quickly be outlined to the people of Northern Ireland.
In that context, he would welcome any move towards "some form of heads of agreement" as an indication of what the eventual outcome was likely to be.
It has been reported that the two governments are planning to propose such heads of agreement at the talks next week.
Mr Trimble was speaking yesterday at the Northern Ireland Forum for Political Dialogue, which is attended by all the main unionist parties, the Alliance Party and the Women's Coalition. He said it was important to show "very quickly" where the process was going.
The best way for the British government to restore confidence in the community was to give assurances that the process would not be determined by the exercise or threat of violence, but by democratic debate and decision making, he said.
"It is essential that government shows that they are prepared to move forward in a process based on democratic principles, and moving towards an outcome that is acceptable to the greater number of people in Northern Ireland," Mr Trimble said.
He did not make any reference to the visit yesterday by the Northern Secretary, Dr Mo Mowlam, to the Maze Prison.
The leader of the Alliance Party, Lord Alderdice, again criticised Dr Mowlam's decision to meet loyalist and IRA prisoners in the Maze. He said the visit was not in keeping with the fact that the talks process was supposed to be based on the Mitchell principles of democracy and non-violence. A threat to return to violence was in breach of those principles.
"I don't believe the paramilitaries will make a decision on their ceasefire on the basis of what the Secretary of State does," said Lord Alderdice, adding that he did not believe the UDA/UFF were going to officially break their ceasefire but that it had already been broken "unofficially".
The Alliance Party leader and members of the Democratic Unionist Party, which also criticised Dr Mowlam's visit, were attacked by Mr Hugh Smyth, of the Progressive Unionist Party, which has links with the UVF.
He said Lord Alderdice had himself visited loyalist prisoners and that in the 1970s members of the DUP "broke their necks to go down to the jail to be seen talking to loyalist prisoners".
Mr Gary McMichael, of the Ulster Democratic Party, which has links with the UDA, said his party was committed to a democratic settlement and admitted that Dr Mowlam's decision to meet prisoners was risky.
He said if the current crisis could be overcome, it would have to be determined within the next few weeks whether an agreement was possible within this negotiating process.