The British and Irish Governments still face some "very difficult" issues in bridging the gap between the DUP and Sinn Fein, the Northern Ireland Secretary has said.
Paul Murphy and Dermot Ahern met in Dublin
Paul Murphy was speaking on Wednesday after discussing efforts to restore devolution in Northern Ireland with Irish Foreign Minister Dermot Ahern.
Mr Murphy said both governments were determined to continue their efforts and he hoped the outstanding difficulties could be resolved within weeks rather than months.
It came a day after Mr Ahern said he hoped for an improvement in the political situation but could not guarantee it.
He said both governments aimed to bring an end to paramilitarism and to restore and stabilise the political institutions.
The institutions in Northern Ireland were suspended two years ago amid allegations of IRA intelligence gathering at the Northern Ireland Office.
On Monday, Mr Murphy said a breakthrough in the political process could be just weeks away.
He said he thought the DUP was prepared to share power with Sinn Fein and a major IRA decommissioning move could be imminent.
BBC Northern Ireland political correspondent Martina Purdy said Sinn Fein and the DUP claimed to be "puzzled by the optimism" coming from the governments over the possibility of an imminent resolution.
"While republicans have apparently made an unprecedented offer to deliver acts of completion over the IRA and its weaponry, in exchange for the full implementation of the Good Friday Agreement, the structures of power-sharing have remained contentious," she added.
She said the two governments had been drawing up a paper aimed at closing the gaps.
Talks aimed at restoring a Stormont government took place
"The governments believe that failure to break the deadlock could lead to a long period of stalemate," she said.
The sticking points have included the method of electing a first and deputy first minister, a date when the assembly can control policing, and whether or not 30 assembly members can challenge ministerial decisions.
On Monday, Sinn Fein's Martin McGuinness said he had "grave concerns" about the position of the British and Irish Governments over possible changes to the institutions.
SDLP leader Mark Durkan warned the governments against imposing proposals on the political parties in the next few weeks.
At the conclusion of intensive political talks at Leeds Castle in Kent last month, Prime Ministers Tony Blair and Bertie Ahern said the thorny issues of IRA disarmament and future paramilitary activity appeared to be resolved.
However, the two governments were unable to get the Northern Ireland Assembly parties to sign up to a deal over power-sharing after unionists and nationalists clashed over future devolved institutions.