Mr McGuinness said he did not believe that the IRA would respond to the Ulster Unionists' demands for a start to decommissioning because that would represent a surrender.
"In my view there isn't even the remotest possibility of the IRA responding to this unilateral demand from the leader of the Ulster Unionist Party, which amounts to ... a demand for the surrender of the IRA," he told BBC1's On The Record.
The 10 March deadline for the start of the new Assembly's executive is now only days away but the Ulster Unionists have so far refused to countenance the presence of Sinn Fein "ministers" unless the IRA first starts giving up its weapons.
Mr McGuinness argued that, under the terms of the Good Friday Agreement, the responsibility to bring about decommissioning did not rest with Sinn Fein alone, and that the two governments and the talks' chairman, Senator George Mitchell, had made clear that the participants would share the task.
"They didn't make it Sinn Fein's responsibility, they didn't make it Martin McGuinness's responsibility - they gave that responsibility to all the participants," he added.
His comments were backed by Sinn Fein supporters at a rally in Belfast yesterday who accused Unionists of delaying the establishment of a power- sharing executive: "We are sick, sore and tired of blocking, stalling, prevaricating, making deals, then backing out of deals and constantly attempting to re-write the Good Friday Agreement," the Sinn Fein chairman, Mitchel McLaughlin, told the rally of about 2,000 people.
He said that Unionism was almost evenly split between those who supported the Good Friday Agreement and those who opposed it and that, although it could delay the process of change, "it cannot stop the momentum for change".
Mr McLaughlin said that Unionists only had a natural veto by virtue of their political numbers in the Assembly and warned the British and Irish governments against drafting any additional veto on to the Good Friday Agreement.
n Detectives investigating the Omagh bombing arrested a woman in Dublin yesterday, bringing the number of people held in connection with the atrocity to four.
The woman and three men were being detained last night under Section 30 of the Offences Against the State Act, which allows police to keep a suspect in custody for up to three days.
The men were arrested over the weekend in the border town Dundalk, Co Louth, after a series of police swoops on both sides of the Irish border in the past eight days. Last week, Colm Murphy, a 48-year-old builder and publican from Co Louth became the first person to be charged in connection with the bombing.Reuse content