The anti-agreement Unionist, Mr Jeffrey Donaldson, has questioned whether Saturday's IRA statement marks the start of a process that will see actual decommissioning of weapons.
"There is nothing in this IRA statement which indicated they are going to disarm their illegal weaponry," he said. "That is what we need to know and it is not enough for the IRA simply to offer conditional access to some of its arms bunkers to a couple of observers from the international community. "
The Lagan Valley MP said total disarmament by all paramilitary groupings was what all of the participants signed up to in the Mitchell Principles and the Belfast Agreement.
"The problem is the IRA still retains possession of these weapons. There is no guarantee that all of the weapons will be deposited in bunkers or that the IRA will not use them during the weeks in between the proposed inspections."
The IRA statement fell far short of the unionist requirement that all paramilitary weapons be verifiably disarmed. He also pointed out that the Ulster Unionist Council required the retention of the full name of the RUC before the re-establishment of government.
"It is absolutely essential that the government listens to what is the clear view of the overwhelming majority of people in Northern Ireland who want the full name of the Royal Ulster Constabulary retained and the traditional symbols connected with the force kept in place."
Another Ulster Unionist MP and opponent of the Belfast Agreement, Mr William Thompson of West Tyrone, said he would have to reject the deal on what he had heard so far. "They are not actually going to give up any arms. And they're only talking about a number of dumps, not all.
"These are illegal weapons and should be completely destroyed. Somewhere down the line what's going to stop Sinn Fein/IRA deciding they don't like what's happening and getting them out and using them again?"
UK Unionist leader Mr Robert McCartney said the statement by the Prime Minister, Mr Tony Blair, at Hillsborough represented "the ultimate surrender to all IRA demands and the final abandonment by the British government of any principled stand on the decommissioning issue.
"In return for a form of words totally without sanction or definitive timetable, and accompanied by a promise to terrorists of substantial demilitarisation, the British government is prepared to meet every terrorist demand to prevent IRA bombs in London. "Every conceivable concession to republicanism has been made and no concession of any kind has been made on any issues considered fundamental to unionist opinion. If the UUP agrees to these proposals, it will have signalled the destruction of the union and the primacy of terror.
"The statement contains nothing that will ensure the destruction of terrorist weaponry, and represents the final surrender to terrorist demands," he said.
The Northern Secretary's intention to re-establish the institutions of government was "the latest surrender to the IRA", DUP councillor Mr Sammy Wilson said. "Instead of no guns, no government, we are now to have government and no guns," he said.
"It is little wonder republicans have welcomed this deal. Once again the rules have been changed to suit them and once again it seems the UUP negotiators have allowed the Labour government and the republicans to beat them into submission."