The new Labour Party leader, Mr Pat Rabbitte, has called for an all-party motion urging the disbandment of the IRA, saying this would tell it "to get off the backs of the people for once and for all".
In his first statement on Northern Ireland as party leader, Mr Rabbitte said he would follow "the constructive position of my predecessor, Mr Ruairí Quinn, in offering full support for the principles of the Good Friday agreement, but I will not hesitate to ask the difficult or awkward questions where these need to be posed".
He said there must be an absolute demonstration from the republican movement of its commitment to exclusively peaceful and democratic means. At the same time there was an urgent need for the Ulster Unionist Party "to accept that the unique circumstances of Northern Ireland require for the foreseeable future the sort of institutionalised power-sharing provided for in the Good Friday agreement".
Mr Rabbitte acknowledged the "remarkable progress" made by Sinn Féin under Mr Gerry Adams and Mr Martin McGuinness.
"But not all members of the republican movement seem to have made the full transition to exclusively peaceful and democratic means."
He said some elements of Mr Adams's speech at the weekend suggested "that he also has some ground to make up. For instance he says that the IRA will not respond to ultimatums to disband from the British government or David Trimble.
"But Mr Adams chooses to ignore the reality that the demand that the IRA disband is being made by the overwhelming majority of the Irish people, North and South," he said.
An effective way to make this point would be through an all- party Dáil motion which, he said, he was confident would be supported by virtually all members of the Dáil.
He said he would engage constructively with all parties in Northern Ireland and looked forward in particular "to maintaining and developing good relations with our sister party in Northern Ireland, the SDLP, whose party conference I hope to attend this weekend".