Taoiseach Bertie Ahern said today the statement issued by the IRA last night was "horrific and shocking".
The statement said the organisation had offered to shoot those responsible for the murder of Belfast man Robert McCartney but his family said they did not want to see such action take place.
"We all want to see justice to be done but their (IRA) response to that was to eliminate three or four people. It's horrific.
"I have to say I was shocked last night and I read that statement more than once.
"This is a democratic society and we all want to see the rule of law operate."
Mr Ahern added that senior civil servants who had worked with him on the peace process over many years did not believe such a statement would come from the IRA. He said: "They just did not believe it.
"The statement, probably is, as the IRA see it, factually the position. That's what the shock is. Maybe we shouldn't be shocked but that's the position and it's a fairly horrific way of setting out the position."
British prime minister Tony Blair said the IRA statement "defies any description".
He told the Commons: "It was a quite extraordinary thing to say. It cannot be in any shape or form justified.
"And there is no way we can make any progress in Northern Ireland that includes Sinn Fein unless there is a complete and total end to violence of whatever kind."
Democratic Unionist Party leader the Rev Ian Paisley said Mr Blair's condemnation of the IRA was "useless" without firm action against the Provisionals. IRA members should be questioned by police over the statement, he demanded.
Northern Ireland chief constable Hugh Orde said the IRA statement that it would "shoot" people meant to kill. Mr Orde said, "It's what they do - one only has to look at the history of the IRA. They have killed thousands of people."
Mr McCartney's family is due to respond formally to the latest IRA statement today.