The DUP leader, the Rev Ian Paisley, said "some progress" was made during a "positive" meeting with the Northern Secretary, Mr Paul Murphy, at Stormont yesterday.
Both Dr Paisley and Mr Murphy characterised the meeting in an affirmative manner although one British source said neither the DUP nor the Northern Secretary addressed the issue of whether the forthcoming review of the Belfast Agreement would amount to a renegotiation, as the DUP is demanding.
Dr Paisley also sought a meeting with the British Prime Minister, Mr Tony Blair, "to ensure that he understands our position and respects the positive agenda we are pursuing".
Mr Blair is expected to grant this request and also to meet the other main Northern Ireland leaders before Christmas.
Dr Paisley said he wanted assurances that at future talks on the agreement, "no limitations will be imposed that would impede us from dealing with the many important issues that need to be addressed. The people we represent have voted for constructive change. We are committed to work for the implementation of our electoral pledges.
Dr Paisley added: "The negotiating context must afford us the opportunity to raise all the concerns of the unionist community, address all the flaws of the old agreement, enable us to reach our objectives and achieve the goals we have set."
Mr Murphy said after the meeting that DUP politicians were "realists" and understood "what it is we have to deal with".
The review would be on the operation of the workings of the agreement, he added. He told BBC Radio 4 that violence was becoming a thing of the past in Northern Ireland and it was not impossible that Sinn Féin and the DUP could share power.
"Over the last six or seven years, all sorts of things have happened here in Northern Ireland which people have said would never have happened and they have," added Mr Murphy.
Sinn Féin's new Assembly team of 24 members - up by six from the first Assembly election five years ago - gathered in Stormont yesterday.
The Sinn Féin president, Mr Gerry Adams, told the MLAs that republicans were determined to see the Belfast Agreement implemented and that there could be no renegotiation of the accord.
"The DUP can refuse to participate if they wish in the political institutions, that is for them to decide, but they cannot veto the other elements of the agreement," he said. "It is therefore up to Mr Blair, along with the Taoiseach, to proceed with their commitments on policing, the criminal justice system, demilitarisation, the equality agenda, human rights, the Irish language and other matters, including OTRs \."
He believed a way through the difficulties could be found.