The First Minister of Northern Ireland, Mr David Trimble, has said he is confident the British government will introduce equivalent anti-terrorist measures to those due to be implemented in the Republic.
He has asked for the Westminster parliament to be recalled, allowing the necessary legislation to be passed.
Mr Trimble also called on the Sinn Fein leadership to go further than its initial condemnation of the Omagh bombing.
"I want to hear something which conveys to the people of Northern Ireland that Sinn Fein are condemning the violence on the basis that it was something they will put behind them permanently and that they are going to follow through all their responsibilities on this," he said.
"I have to say to the republican movement that if they wish to move, this is the best opportunity they have, I hope they take it."
The leader of the Ulster Unionist Party described the spontaneous applause he received at the funeral of the three young boys in Buncrana as "unexpected".
He outlined his presence at the Mass as "an important statement to make on behalf of the whole community of Northern Ireland".
The chairman of Sinn Fein, Mr Mitchell McLaughlin, has called on Mr Trimble to bring the leaders of all political parties together for immediate talks.
"The bombing in Omagh must focus all our minds towards implementing as speedily as possible the Good Friday Agreement," he said.
Mr Sean Farren, the SDLP Assembly member for North Antrim, yesterday highlighted the issue of decommissioning as the only aspect of the Belfast Agreement making no progress.
"Absent until now from the progress list has been any clear sign that decommissioning is underway. While final responsibility for decommissioning lies with the paramilitaries, the parties associated with, or which have any influence, must show that they are working constructively and in good faith to promote decommissioning."
"Failure to demonstrate that commitment could seriously impede overall progress with the Good Friday Agreement," Mr Farren added.
The Democratic Unionist Party yesterday called on the British Prime Minister, Mr Blair, to demand the immediate decommissioning of paramilitary weapons.
"The concessions to terrorism in the Belfast Agreement have seriously compromised Tony Blair's ability to get tough with terrorists," said Mr Ian Paisley jnr, the party's Assembly member for North Antrim.
He described the security measures implemented in the North since last Saturday's bomb attack in Omagh as "a sad farce".
In the aftermath of the Omagh tragedy, Families Against Intimidation and Terror have called for a permanent counselling service to be set up in the town, saying the trauma of the event will remain with the families of the victims for many years.
Meanwhile, Glasgow Celtic Football Club yesterday sponsored a party for 1,200 Catholic and Protestant children at the seaside town of Portrush, Co Antrim.