The Ulster Unionist leader, Mr David Trimble, has called on the British and Irish governments to take a firm line with the paramilitary organisations.
Emerging after an hour of talks with the Taoiseach and the British Prime Minister yesterday, Mr Trimble said unionists' lack of confidence was eroding support for the Belfast Agreement.
"There is a very, very, serious loss of confidence in the unionist community. The two governments need to be active, not passive, in making clear to the paramilitaries that if they cross the red line there will be clear consequences. Otherwise we will have a very serious problem indeed."
The British Prime Minister, Mr Tony Blair, denied that Mr Trimble had given him the end of the parliamentary session as a deadline but said he had agreed to his proposal to make suggestions on how unionist faith in the process could be restored.
He said unionists worried that in the transition from violence to democracy, "somehow we have stopped and the process is now camped at a position where republicans are participating in a democracy that can maintain a certain level of violence.
"That is not acceptable. Transition means transition, full transition from violence to democracy. We now have got to look at the ways we make that clear, that we lay down the clear principles that we have to abide by and what happens if people don't act by what we reflect upon."
Mr Blair said he was convinced the Sinn Féin leadership was serious about making the peace process work, insisting neither his nor the Irish Government wanted to see any party expelled from the process or the political institutions.
The Taoiseach, Mr Ahern, said it was clear there was a collective wish among the pro-Belfast Agreement parties to work together through the implementation group to bring all parts of the agreement to fruition.
"There are difficulties from time to time but what we have to do is expect the difficulties and deal with the difficulties and work in an intense way to find solutions, as we have done in the past, to deal with these issues and I look forward to that," he insisted.
The Sinn Féin president, Mr Gerry Adams, said the onus was on all pro-agreement parties to tackle interface violence and to find solutions to the existing problems in the peace process.
Sanctions would be counter-productive in that undertaking, he added.
While the British and the Irish governments both needed to be far more decisive in their actions against paramilitary violence, such actions should not be linked to sanctions against any political party, the SDLP leader, Mr Mark Durkan, stated.
He also expressed dismay that the Ulster Unionist Party had not stayed to take part in a round-table session attended by all other parties as well as Mr Blair and Mr Ahern.