Sir Reg Empey has held his first meeting as new leader of the Ulster Unionist Party with the British Prime Minister, Mr Tony Blair, in London.
After a meeting in Downing Street with Mr Blair, Ulster Unionist leader Sir Reg Empey said he had warned the Prime Minister not to allow republicans to distance themselves from their criminal operation after the statement.
"We believe there is a risk after the IRA's response to Gerry Adams is issued that they will move to privatise their criminal activities," the East Belfast Assembly member claimed.
"Simply making statements that criminal activity has not been authorised by the leadership of the organisation and has been carried out by criminal elements will not be good enough.
"We will not tolerate any attempt by them to weasel their way out of responsibility for criminal activity."
Sir Reg was commenting as speculation mounted that the IRA will issue a positive statement this week in response to the Sinn Fein leader's call in April for the organisation to embrace democratic and peaceful means exclusively.
Some sources have suggested that the IRA may talk about its members ending active service and instead forming republican clubs.
However, unionists are insistent that all involvement by the IRA in paramilitary and criminal activity must end.
For the Reverend Ian Paisley's Democratic Unionists and Sir Reg's Ulster Unionists that means an end to the recruitment of new members, training, intelligence gathering, targeting, weapons importation and involvement in all violence and expulsions.
They are also demanding an end to IRA involvement in robberies, jewel smuggling, cigarette and alcohol smuggling, the manufacture and sale of pirate DVDs, CDs and computer games and the laundering of money through legitimate businesses.
It is also expected that the IRA will announce a significant act of weapons decommissioning.