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.
Identify obstacles
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.
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.
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.