Devolution is a "real possibility in the near future" Northern Ireland Secretary Peter Hain has said.
The power-sharing executive has been suspended since 2002
Mr Hain and Irish Foreign Minister Dermot Ahern chaired talks with the NI parties at Hillsborough on Monday.
"I'm confident we can make the necessary progress to get the assembly running," he said, adding that he wanted to see progress by April.
The parties will meet the political development minister, David Hanson, for more talks next week.
Mr Hain ruled out recalling the assembly in an attempt to force all-party agreement.
He said he was not prepared to recall the assembly simply to have it "shipwrecked".
Mr Ahern said any deal would be determined by the template of the Good Friday Agreement.
"Obviously we will listen to what the parties have to say and take onboard what their documents have to say," he said.
"But ultimately the overriding template of all of this is the template set by the Good Friday Agreement."
Expectations had been low after last week's Independent Monitoring Commission report on continuing IRA activity.
Speaking after talks, the DUP said the IRA must disband before they entered into government with Sinn Fein.
"There was no agreement between us, there is a great gulf because the southern government still thinks the IRA should be there and by right should be taking part in these discussions and by right should be in any future government of Northern Ireland," DUP leader Ian Paisley said.
Ian Paisley said the Irish government was backing the IRA
"There is no healing of any wounds, as far as unionism is concerned - they are backing the IRA to get them back into government."
Speaking afterwards, Sinn Fein President Gerry Adams said the governments must set out a public time-frame for the restoration of the institutions, before the loyalist marching season begins in April.
"People need to have some sense that local, accountable representatives are administering their affairs," he said.
He said there was a question about whether the two governments were in charge, or whether Ian Paisley was.
Speaking after his party met the two ministers, SDLP leader Mark Durkan called on the two governments to set a deadline for the restoration of the institutions at Stormont.
Mr Durkan said failure to show determination would just allow the DUP to feel that they controlled the political calendar.
"Suspension was created because of the activities of the IRA and the failure to decommission.
"If this has been dealt with, then the cause of suspension, the case for suspension has totally changed, it has gone," he said.
Meanwhile, government sources say a bill which will provide for the devolution of policing and justice to Northern Ireland may be widened to make further changes to the rules of the Stormont institutions.
The Northern Ireland Bill, due to be published on 16 February, is understood to cover policing and some other matters, such as electricity deregulation.
The bill could also be amended in April to make other rule changes.
These changes concern voting procedures at Stormont and the accountability of ministers.
Devolved government at Stormont was suspended in 2002 following allegations of a republican spy ring at the Northern Ireland Office.