Dr Mowlam said prospects for success increased on Friday, when three principles were agreed for the basis of negot-iations resuming tomorrow.
The parties expect tough sessions which will involve five key elements - the British and Irish governments, the Ulster Unionists, Sinn Fein and the Social Democratic and Labour Party.
A hardline tone was maintained yesterday by Jeffrey Donaldson, the anti- Good Friday agreement MP recalled to the Ulster Unionist talks team by party leader David Trimble.
He described Tony Blair's initial proposals for breaking the deadlock as unacceptable, saying no reliance could be placed on the word of republicans.
Mr Donaldson told BBC Radio 4's Today programme: "Opinion now within the party is very firmly fixed on the belief that we have to have a credible beginning to the process of decommissioning before Sinn Fein-IRA can be admitted to the government of Northern Ireland.
"We cannot trust the IRA's word. That is why David Trimble has made it clear we have to see tangible evidence that the IRA are now committed to peaceful means."
President Bill Clinton is maintaining intensive contacts with Tony Blair and the Taoiseach, Bertie Ahern. He said: "This is a very serious, serious period, and I do not want to make it worse. I intend to do whatever anybody thinks I can do to save it.
"I hope and pray the Good Friday Agreement will be saved. The differences, though they are profound, are as nothing compared to the cost of losing it."
n Two men from Northern Ireland have been remanded in custody in Dublin charged with possession of explosive substances near the border.
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