The start of substantive negotiations today offers "a great chance to build a better future for Northern Ireland", the North's Political Development Minister, Mr Paul Murphy, has said.
Speaking in the former parliament buildings at Stormont, Mr Murphy said: "We're not expecting miracles and there are going to be months of negotiations ahead, but we believe that the process has the potential to deliver an agreement. It's vital for people to talk."
He hoped the Democratic Unionists and the UK Unionist Party would rejoin the discussions in the future: "The talks, in themselves, are a threat to nobody."
The three strands of substantive negotiations will start in separate sessions. Strand One, relationships within Northern Ireland, will be discussed in the morning session, chaired by Mr Murphy. Each of the delegations is entitled to make an opening statement.
The Government delegation from Dublin will not be taking part in Strand One but it will join the other participants in the afternoon for the Strand Two discussion on new structures for North-South relationships, chaired by Senator George Mitchell.
In the absence of the Minister for Foreign Affairs, Mr Burke, the Irish delegation will be led by the Minister for Justice, Mr O'Donoghue and the Minister of State for Foreign Affairs, Ms Liz O'Donnell.
The evening session will discuss the "East-West" relationship between the two islands and will be confined to the two governments. However, the other delegations will be kept informed of progress. Next week, Monday will be devoted solely to Strand One; Tuesday to Strand Two and Wednesday to Strand Three.
Asked about reports of an impending visit by the British Prime Minister, Mr Tony Blair, Mr Murphy said: "I am sure the time will come in the not-too-distant future when he will visit Northern Ireland and the talks, bearing in mind of course that I am sure the Taoiseach, too, will be interested in coming to Belfast."
Asked about the current difficulties of Mr Burke, Mr Murphy said: "That is a matter for the Republic of Ireland and the Irish Government. All I have to say is that I have worked extremely well with him in the months that he's been Irish Foreign Minister; for example, all our press conferences where both governments have been involved have been joint press conferences."
Mr Sean Farren, a senior negotiator with the SDLP, called last night on the Ulster Unionists "to have the courage and vision to work with the SDLP and all of the other parties to achieve an historic and lasting settlement".
In a draft statement prepared for today's talks, the Sinn Fein president, Mr Gerry Adams, called for "a democratic peace settlement acceptable to all sections of the Irish people". He said an internal settlement could not work: "There has to be fundamental constitutional and political change."
There was criticism of the weekend statement by Mr Martin McGuinness that Sinn Fein was entering the talks to "smash the Union".