Senior Unionists also say they have been dismayed at what they claim is the pro-nationalist tenor of a British government document which was tabled in last week's talks and leaked at the weekend.
This canvassed several possibilities, one of which was a new north-south institution with executive powers. Such ideas are anathema to Unionists, most of whom see the purpose of the talks as an opportunity to reduce Dublin influence in Northern Ireland.
This document appears to have been tabled without notice by the British government. Unionist negotiators began talks on a line-by-line basis without having read the whole document, then pulled out of talks when they noticed some of its more contentious parts.
James Molyneaux, the Ulster Unionist leader, is said to have been 'hopping mad', when he later read the document and wrote to Sir Patrick Mayhew, Secretary of State for Northern Ireland, demanding its withdrawal. The Government then moved to distance itself from the document, whose status is now unclear.
Unionists remain suspicious of what they allege is its 'green' (ie nationalist) parts, which include a detailed examination of possible north-south links, such as joint institutions with delegated executive responsibility for specific subjects.
Talks are scheduled to resume in Belfast on Wednesday, moving to Dublin next Monday. But the Rev Ian Paisley's Democratic Unionist Party has pulled out of discussions until the agenda reaches Articles 2 and 3 of the Republic's constitution, which lay claim to Northern Ireland.
Mr Paisley is demanding that Dublin should commit itself to holding a referendum on the constitution.
Mr Molyneaux's party remains at the table, but he toughened his position at the weekend by declaring in a BBC interview that discussions could not continue unless Dublin demonstrated its intention of changing the constitution.
He said: 'If it becomes clear in a few weeks' time that the Irish government has no intention of removing its illegal claim to Northern Ireland then we cannot be expected and we simply will not continue with discussions. They will have given a clear signal that the shutters have come down, not us. We could not realistically stay at the table because we would be conning everybody.'
David Andrews, the Irish Foreign Minister, said yesterday that he was disappointed with Mr Molyneaux's stance. He added: 'Nothing is agreed until everything is agreed, and that was the basis for the talks. It appears to me that what the Unionists are requesting are that Articles 2 and 3 be unconditionally abandoned.'
Meanwhile, senior Protestant and Catholic church leaders, who are anxious about the course of the talks, appealed to all sides to stay at the conference table.
The Catholic Cardinal, Dr Cahal Daly, said: 'The ending of the talks would be disastrous and I do not know what the consequences might be.'
Dr Robin Eames, Archbishop of the Church of Ireland, said: 'My plea is: in God's name, and in the light of history, keep at it until you have exhausted every conceivable possibility for agreement.'
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