The Stormont committee has failed to elect a chairperson
They broke up on Wednesday after two and a half days of talks and the issue will now be referred to Northern Ireland Secretary Peter Hain.
The SDLP blamed the DUP for the impasse claiming the party had "blocked all efforts to resolve the issue".
However, the DUP said they "had made every effort to get agreement".
Mr Hain said it was impossible to see the assembly moving on substantive business "if there could not be agreement on such a basic procedural issue".
"Restoring devolution is not for the benefit of the British or Irish governments, it is not for the benefit of MLAs, it is for the people of Northern Ireland," he said.
Blame
"The very least they have a right to expect is that the MLAs they elected would do the job they elected them to do."
The DUP has taken most of the blame from the other parties for the deadlock.
A DUP spokesman said the party had wanted Speaker Eileen Bell to take the post, but she refused.
He said they also made a number of suggestions which were rejected by the other parties.
"We made every effort to get agreement and to make the committee work," the spokesman said.
"However, it has become clear that there were those who not only wished to control the agenda of the committee, but they also wanted to have a guaranteed chairmanship at a guaranteed time."
Obstacles
Sean Farren of the SDLP said consensus had been reached among all parties except the DUP which had "obstinately held on to the politics of veto".
"Yet again the DUP, instead of helping to remove obstacles to devolution, have shown themselves to be nothing but obstructive and lacking in any spirit of co-operation," Mr Farren said.
Sinn Fein's Martin McGuinness said the government should not wait until its November deadline to close the assembly if agreement could not be reached soon.
"If the DUP is not prepared to do the business or give any substantive indication in the course of June, then the British government would be as well stopping the salaries at the end of June," he said.
Alan McFarland of the UUP accused the DUP of a "lack of vision and determination for progress to be made".
"The prevarication and petty wriggling by the DUP is preventing the potential for progress and holding us all up to public ridicule," he said.
Alliance Party leader David Ford said no-one on the committee had a right to demand their own way.
"The practical reality is that the two biggest parties have not shown they are prepared to move forward at all," he said.
The committee's role is to identify obstacles to the return of devolution.
Earlier on Wednesday, Sinn Fein said they would demand another vote on the posts of first and deputy first minister before the assembly broke up for the summer.
The vote could take place about 19 or 20 June, the week before a scheduled visit by the two prime ministers to Stormont.
On 15 May, Northern Ireland's politicians took their seats in the Stormont assembly for the first time since October 2002.
A bid to elect a first minister and deputy first minister failed to gain the necessary cross-party support.
While there is no immediate prospect of a power-sharing executive being formed, the government hopes recalling the politicians will help to pave the way towards a deal in the autumn, by its deadline of 24 November.
Devolved government was suspended over allegations of a republican spy ring. The court case that followed collapsed.
Direct rule from London was restored in October 2002 and has been in place since.
Logo of the Northern Ireland Assembly.
After three days of talks, parties in Northern Ireland have come to a stalemate over the election of a chairperson for a committee to help setup a devolved government in Northern Ireland. It is now up to Northern Ireland Secretary of State Peter Hain to choose the next course of action.

The committee, known as the Preparation for Government Committee, convened Monday to begin its first task: the election of a chairperson for the committee. Its main task however is to help set a roadmap for devolved government in Northern Ireland. The committee is made up of the two republican parties (Sinn Féin and SDLP), the two unionist parties (DUP and UUP) and the non-sectarianist Alliance Party.

Sinn Féin's proposal is for the chairpersonship to revolve between them and the Democratic Unionist Party. However, the DUP refused that proposal.

The DUP proposed that Speaker of the Assembly Eileen Bell should be the chairperson. However, Bell stated that it would inappropriate for her to take the post and refused. They also suggested the DUP MP for South Antrim William McCrea and Alliance Party leader David Ford as possible candidates.

Peter Hain called the refusal of parties to cooperate "frustrating."

Sinn Féin, SDLP and the Alliance Party have all blamed the DUP for the failure.

"Yet again the DUP, instead of helping to remove obstacles to devolution, have shown themselves to be nothing but obstructive and lacking in any spirit of co-operation, "said Sean Farren of the SDLP.

Mark Durkan, the leader of SDLP, has criticized both Peter Hain and the DUP and its leader, Ian Paisley on Monday.

"If the DUP is not prepared to do the business or give any substantive indication in the course of June, then the British government would be as well stopping the salaries at the end of June," said Sinn Fein's Martin McGuinness.

"The practical reality is that the two biggest parties have not shown they are prepared to move forward at all." said David Ford, the leader of the Alliance Party.

"The prevarication and petty wriggling by the DUP is preventing the potential for progress and holding us all up to public ridicule." said Ulster Unionist Party's Alan McFarland.

On Monday, Ian Paisley asked for extension of the November 24 deadline fot two weeks. It was refused.

This is part of plan by British Prime Minister Tony Blair and Irish Toaiseach Bertie Ahern to set up a devolved government in Northern Ireland after its assembly was suspended in October 2002 over allegations of a IRA spy ring.

If a plan for devolved government is not setup by November 24, direct rule from London will continue with greater input from the Republic of Ireland.