The UUP leader, Mr David Trimble, and Sinn Fein's chief negotiator, Mr Martin McGuinness, have both expressed cautious optimism that agreement can be reached on decommissioning and the setting up of an executive in Northern Ireland.
But with talks between the pro-agreement parties set to resume tomorrow, Mr Trimble yesterday described recent IRA statements, omitting reference to its position that it would never decommission weapons, as "not unambiguous", and Mr McGuinness warned that Sinn Fein could not deliver support for a renegotiation of the Belfast Agreement.
The Minister for Foreign Affairs, Mr Andrews, and the junior Minister, Ms Liz O'Donnell, will join the Northern Secretary, Dr Mo Mowlam, and the North's politicians for tomorrow's talks. The Taoiseach, Mr Ahern, and the British Prime Minister, Mr Blair, could also travel to Belfast on Thursday.
According to Mr Trimble, republicans must now show their true commitment to the Belfast Agreement by starting to disarm. "I hope we will get down to real progress sooner rather than later. In the words of Bertie Ahern, people didn't vote for an armed peace, they want a real one, and it's time it was delivered."
The North's First Minister said he was concerned at a statement by the UVF leadership last week refusing to consider any immediate arms hand-over. If paramilitaries at least set a date for decommissioning it would be a step forward, but "it wouldn't be satisfactory to me".
He rejected any suggestion that the RUC or British army would give up weapons as part of the Hillsborough Declaration's proposed "collective act of reconciliation". "There is absolutely no equivalent between arms held by the army and police and those held by illegal organisations."
Mr McGuinness said he would enter this week's talks in "a positive and constructive frame of mind" but said the Hillsborough Declaration represented an unacceptable attempt to link decommissioning with Sinn Fein's taking up ministerial office. He also accused the British government of a too-slow "drip, drip" approach to demilitarisation.
He warned of the dangers of letting the peace process drift into the summer marching season, and the June 10th European election which the DUP leader, the Rev Ian Paisley, has pledged to turn into a second referendum on the Belfast Agreement.
Over the weekend, senior Provisional sources said they were unimpressed with the Hillsborough Declaration. In a number of press briefings, they claimed it marked a failure on the part of both governments to confront the UUP's "veto" on political progress. They said there was anger among republicans at how the declaration was being presented by the two governments.
The Ulster Unionist Assembly team meets today for discussions in advance of tomorrow's resumption of talks. Several UUP Assembly members have voiced concern about the Hillsborough Declaration. They included Ms Pauline Armitage, a close associate of the anti-agreement MP, Mr Willie Ross, Mr Roy Beggs jnr, Mr Billy Armstrong and the party's deputy chief whip, Mr Derek Hussey.
They believe that the declaration does not clearly demand decommissioning by the Provisional IRA before Sinn Fein can enter a Northern executive. The UUP is expected to ask both governments to clarify the exact meaning of the declaration, which outlines the intention for some paramilitary arms to be "put beyond use".
The Archbishop of Armagh, Dr Sean Brady, meanwhile has called on the North's politicians to find "an honourable way" to overcome the current obstacles to political progress.
Dr Brady stressed that political consensus on decommissioning must be achieved before the proposed act of reconciliation. "If the required agreement is not reached then the act of reconciliation could appear premature. True peace consists in genuine reconciliation," he said.