The DUP leader, Reverend Ian Paisley, has said the suggestion that the IRA has completely disarmed is a blatant lie.
Speaking at his party's annual conference in Belfast, Dr Paisley said there would be no executive with Sinn Féin as long as the IRA was, as he put it, in business.
He said the fall-out from last week's report from the Independent Monitoring Commission had justified his scepticism about the IRA.
Dr Paisley said the DUP would go into talks at Hillsborough on Monday determined to defend the principle of fairness.
He also said unionists would not be prepared to make any deal with those who have links to criminality.
Earlier, DUP deputy leader, Peter Robinson, said that the Good Friday Agreement was dead.
He told the conference that the British government should be ashamed of how it handled concerns about ongoing IRA criminality, violence and allegations that they had held on to their weapons.
Mr Robinson said that last Wednesday's report on paramilitary activity had shown that the IRA had still a very long way to go before republicans could democratise.