The failure to elect a chairperson for the Preparation for Government Committee raises serious questions, NI Secretary Peter Hain has warned.
The Stormont committee is to help prepare a return to devolution
The committee broke up after an acrimonious first meeting at Stormont without reaching agreement.
Mr Hain said this "must cause those who elected them to question their commitment to getting back to work".
Both Sinn Fein and the Alliance Party have accused the DUP of adopting a negative attitude to the committee.
Sinn Fein's Martin McGuinness said his suggestion that the body either be chaired jointly by the DUP and SF or rotated was rejected by the DUP.
The DUP denied allegations it was not serious about making progress.
The committee, whose role is to identify obstacles to the return of devolution, will reconvene on Tuesday.
Mr Hain said the assembly would also meet as planned to discuss industrial rating on Tuesday.
He added: "I will want to see what progress the Preparation for Government committee makes before deciding on future assembly business."
Mr Hain said he had asked Northern Ireland Assembly Speaker Eileen Bell to "talk to the parties urgently to resolve the issue of how to chair the committee".
The DUP wanted Ms Bell as chairperson, but she has rejected this role and left Monday's proceedings to be handled by an assembly official.
They also suggested DUP South Antrim MP William McCrea and Alliance Party leader David Ford as possible chairpersons.
However, Mr Ford has said that he would only consider the role as part of a wider rotation system.
Some of the parties are writing to Mr Hain to clarify whether the need for "consensus" means the committee can only move forward on the basis of unanimity.
DUP leader Ian Paisley said it was untrue that it had not sent important figures to the first meeting.
Peter Hain invited the main parties to send three representatives
Earlier, Mr Paisley said he would ask the government for a two-week extension to the November 24 deadline to devolution in Northern Ireland.
Mr Paisley said the politicians should get "injury time" because the government has not scheduled any business at Stormont for the past two weeks.
However, Mr Hain said there was "no question of further government legislation to amend the deadline, which is set in statute".
Martin McGuinness is to sit on the cross-party committee alongside senior members from other parties.
Mr Hain has invited the four main parties to each send three representatives.
The Alliance Party has been given two places.
The DUP has insisted that the committee should not be a negotiating body, while the SDLP wants it to do precisely that.
Alliance Party leader David Ford said he had reservations about the committee, but would join.
'Pave the way'
On Sunday, Ulster Unionist Party leader Sir Reg Empey said he had appointed Alan McFarland, Danny Kennedy and Michael McGimpsey to represent the party on the committee.
"Although we still remain concerned at the manner in which the remit for the committee has been arrived at, we will approach it in a positive manner and seek to identify the obstacles that are standing in the way of devolution and deal with them," he said.
On 15 May, Northern Ireland's politicians took their seats in the Stormont assembly for the first time since October 2002.
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.