The DUP has reacted "with contempt" to calls from the Sinn Féin president for the two governments to act if the Northern parties fail to agree on the restoration of Stormont.
Mr Gerry Adams, addressing supporters in New York on Thursday, said London and Dublin should share power in Northern Ireland if what he called "rejectionist" unionists obstructed the peace process.
If the Democratic Unionists refused to agree on the return of devolution, Mr Adams said London and Dublin should press ahead with the full implementation of the Belfast Agreement and dissolve the Assembly, if necessary.
"It's not just parties who can share power, governments can share power also," he said.
"The British and Irish governments must look to formal institutionalised power sharing at governmental level," he added.
The demand for dissolution of the Assembly and a form of joint authority over Northern Ireland has enraged the DUP.
Mr Maurice Morrow, a Fermanagh Assembly member, said: "Any notion of joint authority or anything that resembles it is pie in the sky. Arrangements for the governance of Northern Ireland will only work where there is agreement from both unionists and nationalists." He said unionists could take heart from the fact that Mr Adams was demanding that the British and Irish governments intervene.
"Sinn Féin/IRA have realised that for the first time in this process, the unionist community is being represented by a party who will not be rolling over to accept anything less than an end to terrorist and criminal activity and devolved structures that are fair to both unionists and nationalists," he said.
He claimed: "The days of Sinn Féin/IRA getting their way on everything are over."
The SDLP also criticised Mr Adams's comments, but from the point of view that they did not go far enough.
Dr Seán Farren, the party's senior negotiator, said the DUP did not appear to want an agreement after "spinning" for months.
"That is why Sinn Féin, like ourselves, are right to be looking at how we can be getting as much of the agreement now as we can," he said.
However, Dr Farren criticised what he called Mr Adams's "vague proposals for power-sharing by the governments".
He said: "Far better are the SDLP's proposals for ending suspension and getting the agreement moving." The SDLP's plans for appointed commissioners to take the place of a power-sharing Executive would "send the direct rulers packing", he said.