Ms Mowlam said the terrorists must declare an "unequivocal ceasefire" or Sinn Fein would be left behind in the attempts to reach a political settlement .
The Government had pinned its hopes on a "new mood" after tens of thousands of Orangemen paraded without confrontation. But over the weekend petrol- bombs were thrown and several Royal Ulster Constabulary officers were wounded during rioting in Londonderry and Belfast.
The renewed violence confirmed Unionist beliefs that a new ceasefire is unlikely and that Sinn Fein should not be allowed to enter the multi- party talks. The Ulster Unionist leader, David Trimble, yesterday called for an end to what he called "wishful thinking" .
"There are too many people still engaged in wishful thinking and the consequences of their wishful thinking are likely to be very bad for this community," he told BBC's Breakfast with Frost.
He warned that some Unionists believed the Government's agenda was simply to get Sinn Fein into the multi-party talks.
John Hume, leader of the nationalist Social Democratic and Labour Party, accused Mr Trimble of being "negative", although he agreed that Sinn Fein had to commit itself to peaceful means to gain entry to the Stormont talks.
He urged the IRA to call a total end to its campaign of violence. And he praised the "moral courage" of Ulster Orangemen for re-routing or calling off marches this weekend. "It was a very praiseworthy decision and I think it enormously improved the atmosphere in the communities involved," he said.
Ms Mowlam accepted that Mr Trimble would find it hard to conceive of a ceasefire.
"Let us just deal step-by-step with where we're going. Let's make sure we have a political process to offer the people of Northern Ireland that the constitutional parties are engaged in," she said. "And let the IRA, Sinn Fein, make their decision. The ball's in their court. We can't decide for them."
Yesterday the Prime Minister, Tony Blair, urged Sinn Fein to "opt for hope" by responding to the Orangemen's action. Substantive talks are due to begin in September, and the Government has made clear that any ceasefire must last at least six weeks and has to be genuine "by word and deed".
Ms Mowlam drew hope from the possibility of agreement on the issue of decommissioning when the multi- party talks begin again tomorrow. She said the "good news" was that the parties currently engaged in the talks had agreed a timetable for the issue to be determined.
"What's important is that the peace process itself gets in gear and people see some momentum being reached by that," Ms Mowlam told Sky's Sunday programme with Adam Boulton.
n Security forces last night found several hundred pounds of explosives on the nationalist Creggan Estate in Londonderry. The explosives were hidden in a coal shed and wrapped in plastic bags. Houses in the area were evacuated by police.Reuse content