The Northern Secretary, Mr Peter Mandelson, has warned that the Belfast Agreement is "the only show in town" and said he remains hopeful that this week's talks in London can bring progress.
Speaking before detailed talks in Dublin yesterday with the Minister for Foreign Affairs, Mr Andrews, Mr Mandelson said there was no alternative to the agreement and rejected suggestions that there was a "Plan B" should Senator George Mitchell's attempts to break the deadlock fail.
Both men said they were optimistic about the outcome of the Mitchell review, with Mr Andrews saying he was "very optimistic indeed".
The two ministers and the Minister of State at the Department of Foreign Affairs, Ms Liz O'Donnell, had talks for 80 minutes on the Mitchell review, the Patten report on policing and the continuing stand-off in relation to the Garvaghy Road Orange march in Portadown.
Mr Andrews also raised the controversies over the 1989 killing of the Belfast solicitor, Mr Pat Finucane, and the 1997 beating to death of a Portadown Catholic, Mr Robert Hamill.
Speaking before the meeting, Mr Mandelson said the Belfast Agreement "remains the only show in town. It settled the constitutional issues once and for all. It provides a way forward. It is the basis for change and for an unbreakable peace in Ireland". The possibility of implementing the agreement in full "remains within our grasp", he said.
"That's why the Mitchell talks this week are so important. I hope those involved realise they have to offer clarity and certainty to all sides. I remain hopeful but, whatever happens, our relationship and the close working co-operation between the two governments will go on regardless."
Mr Andrews paid tribute to Mr Mandelson's predecessor, Dr Mo Mowlam.
"Relations between the Irish and British governments have been hugely warmed over the past couple of years," he said, and much of this was due to the work of Dr Mowlam.