Northern Ireland's political parties generally agree that devolution should be restored in the province, the secretary of state has said.
Sinn Fein and Democratic Unionist teams at the opening session
Paul Murphy was speaking after the opening session of a review of the 1998 Good Friday Agreement at Stormont.
Northern Ireland's political institutions have been suspended since October 2002.
The main trigger was allegations of IRA intelligence gathering in the Stormont government.
The British and Irish governments and the political parties read opening statements at a round table meeting.
Mr Murphy said it had been a very positive start to the review on Tuesday.
"There was generally an agreement that there should be a return to devolution," he said.
"The point was very clearly made that people in Northern Ireland want locally elected, locally accountable ministers to do the job that I and my fellow ministers are doing in direct rule.
"Obviously the issue of the lack of confidence and lack of trust which has characterised the last year or so is an issue that we have to address, and most parties made that point."
Mr Murphy also said the issues of paramilitary activity and the stability of the institutions also had to be addressed.
Paul Murphy and Brian Cowen are chairing the review
Irish Foreign Affairs Minister Brian Cowen said one of his government's priorities was to see devolution restored as soon as possible.
"The review is a valuable opportunity to collectively take stock and assess where the operation of the Agreement can be improved," he added.
The parties differ about what form the review - expected to run until Easter - should take, with the DUP saying it will not negotiate with Sinn Fein.
After the opening session, DUP leader Ian Paisley said: "Today was the farce of everyone making a statement. It was only to please
the governments, to let them say they got everyone in the same room."
When the 1998 Agreement was signed it contained a commitment that a conference should be held four years later to review and report on its operation.
But Stormont has been suspended four times and replaced with direct rule for the past 14 months.
The SDLP and Sinn Fein say the Agreement cannot be renegotiated and that the review should be short.
The Ulster Unionists say it should deal with the problem which led to suspension in the first place - paramilitary violence - while the DUP want a wholesale renegotiation.
They sat at the table to join the other parties in reading an opening statement, but said they would only meet parties other than Sinn Fein and the two governments.
This is a problem for the co-chairmen, the Northern Ireland Secretary, Paul Murphy, and the Irish Foreign Affairs Minister, Brian Cowen.
Prior to the meeting, Ulster Unionist leader David Trimble said the DUP was "turning a blind eye to paramilitarism".
"We have heard from people saying that the objective is not to get decommissioning - that they want to have institutions which continue no matter what Sinn Fein do," he said.
Sinn Fein President Gerry Adams said the review should be about better delivery of the Agreement.
"The review was always envisaged to be taking place in a context where the institutions were up and running and the process was ongoing," he said.
Meanwhile, Sinn Fein's chief negotiator Martin McGuinness is understood to have had a meeting in Downing Street on Monday.
Mitchell Reiss is holding talks with party representatives
The party has refused to give further details.
The DUP and Sinn Fein emerged as the two largest parties after last November's assembly election.
The government is talking about the possibility of holding another election if there is no progress.
The US president's new special envoy to Northern Ireland is set to closely monitor the progress of the review.
Mitchell Reiss held talks with representatives of the political parties on Tuesday, after meeting Paul Murphy on Monday.
Later in the week, he will travel to London and Dublin to meet the two governments.
Speaking after the meeting Dr Reiss, SDLP leader Mark Durkan said: "We raised our concerns with Dr Reiss about Tony Blair's handling of the Cory report. The British Government is in blatant default of its commitment to publish Cory and hold inquiries."