If the IRA does not begin to decommission over the next six weeks, the Ulster Unionist Party will move to exclude Sinn Fein from the Executive, Lord Taylor said yesterday.
He was addressing the Assembly following a personal statement by Mr Seamus Mallon.
The "next stage of developments" would come into force if illegal firearms and arsenals were not put beyond use over the coming weeks, Lord Taylor said.
"That will be to consider the exclusion of those parties from the Executive who are linked with paramilitary groups which still retain their firearms and their bombs, irrespective of the desire of the people of Northern Ireland."
The DUP deputy leader, Mr Peter Robinson, echoed the call for Sinn Fein's expulsion.
"While the Provisional IRA hold on to their weapons, their machine intact, Sinn Fein, their partners, are not entitled to be part of the democratic process, never mind being part of government. Until that moment arrives, then they do not have a democratic mandate", he said.
With neither Mr Trimble nor Sir Reg Empey, the Minister he has designated to exercise the functions of first minister, present at yesterday's debate, attention was focused on the personal statement by Mr Mallon.
Mr Mallon, who will continue to exercise the office of deputy first minister for the next six weeks, paid tribute to Mr Trimble's work in the Assembly but criticised his decision to resign. "I regret that he has chosen to precipitate this latest in a long series of crises," he said.
While Mr Mallon acknowledged Sinn Fein's democratic mandate, he described the IRA's failure to decommission as "shameful".
"Sinn Fein demands respect for its democratic mandate. I respect it, but if the outcome of the best endeavours of Sinn Fein to put weapons beyond use has borne so little fruit, it is clear that the IRA does not respect that mandate and the obligations that go with it," he said.
Both the DUP and the Ulster Unionists also bore responsibility for the current crisis, Mr Mallon said. "The blatant unwillingness of DUP Ministers to undertake the basic responsibilities of ministerial office has been paralleled by deliberate efforts to wreck a carefully constructed institutional balance, particularly through refusal to nominate Sinn Fein ministers to the North-South Ministerial Council."
The Speaker, Lord Alderdice, had earlier confirmed Mr Trimble's resignation. Elections for a new first minister and deputy first minister were to be held within six weeks. "That is by August 11th," he said.