David Trimble plans to collapse the NI Executive
The Ulster Unionist ministers are expected to resign from the powersharing government later this week because of the IRA's refusal to begin decommissioning its arms.
Mr Trimble resigned his position as Northern Ireland first minister in July to put pressure on the republican movement.
He announced two weeks ago that he intended to bring the political crisis to a head by withdrawing the rest of the Ulster Unionist ministers because his party could no longer sit in the executive with Sinn Fein.
The withdrawal of UUP ministers would lead to the collapse of the institutions.
It is expected, however, that Northern Ireland Secretary John Reid would reintroduce direct rule before the assembly collapsed.
If devolution is suspended for an unlimited period, it is likely the government will start a review of the implementation of the Good Friday Agreement, on which devolution is based.
"There is a democratic imperative on all of us and not least David Trimble to ensure that the people's institutions survive," he said.
"And I still believe, even though we have had many difficulties within this process, that there is a very resounding majority of our people out there, unionists, loyalists, republicans and nationalists who want the peace process to continue."
At the weekend Mr McGuinness said he was working "flat out" to achieve IRA decommissioning.
But on Monday he refused to speculate on whether the IRA would make a gesture on decommissioning in advance of the Ulster Unionists withdrawing from the executive.
"The reason why we are in the mess we are in today is because David Trimble has walked away from his responsibilities," he said.
In Washington on Monday Mr Trimble met the United States special envoy to Northern Ireland Richard Haass.
It had just been announced that Mr Haass' areas of responsibility as the US State Department's director of policy planning had been expanded.
He has been appointed US "special coordinator" for Afghanistan, consulting with Afghan opposition groups, the United Nations and others about the composition and type of government that could take over from the Taleban.
Mr Trimble also met US Congressmen and briefed American journalists on the current state of the peace process.
Disarmament 'must be seen'
Meanwhile, DUP leader Ian Paisley has said any act of disarmament by the IRA would have to be verified, permanent and accompanied by the dismantling of the republican paramilitary group's structures to satisfy unionists.
In statement, Mr Paisley said: "If decommissioning is to take place, then it must be seen to be done.
"Too often in the past the unionist population have been deceived by empty words and hollow gestures. Only if any decommissioning is genuinely verified will it satisfy the unionist population.
"Decommissioning must also be permanent. There must be no way back for the weapons and explosives to be recommissioned. Tricks with smoke and mirrors will not dupe the unionist people."