The DUP is asking the chief of the arms-decommissioning body how old the IRA weapons he saw put beyond use were, party leader Ian Paisley has said.
Ian Paisley says he has questions about the age of IRA weapons
He is meeting General John de Chastelain over his report that the IRA has now decommissioned all its weapons.
Northern Ireland Secretary Peter Hain said unionist distrust was "natural", but the IRA's "historic move" brought the return of devolution closer.
Sinn Fein's Martin McGuinness is going to the US to brief Irish Americans.
The SDLP, the Ulster Unionists and the Alliance Party also have appointments with the general and his fellow commissioners on Tuesday.
Mr Hain said he could understand Mr Paisley's scepticism, but asked him to respect the integrity of General de Chastelain.
"I wouldn't have expected Ian or the unionists to just bowl over and welcome everything with open arms because they've got a lot of cause to be sceptical and suspicious over the behaviour of the IRA in the past," he told BBC News on Tuesday.
"The IRA have often promised to do things and then reneged on them."
The Independent Monitoring Commission (IMC) reports next month and in January would consider whether the IRA was delivering on its promise to cease paramilitary and criminal activity, Mr Hain said earlier.
"If [the IMC] gives a clean bill of health to the ending and closing down of IRA paramilitary and criminal activity, it will, I think, be very significant and ought then to open the door to proper negotiations to take us forward on a road that will end in self-government and power-sharing."
BBC NI political editor Mark Devenport said: "Unionists have called upon the government to publish the security force estimates of the IRA's arsenal which General De Chastelain relied on to carry out his work.
"However, government sources indicate this is unlikely as the estimates were derived from intelligence which officials would not want to compromise."
But if we want to get rid of that fear, then it's up to the local politicians to step up and deal with the social conditions in the interests of all - you can't just get rid of the guns - there has to be some kind of peace benefit for all
The White House has welcomed the IRA's move as an "important first step" and the US State Department called on all paramilitary groups, whether loyalist or republican, to work with General de Chastelain to bring about complete disarmament.
Spokesman Sean McCormack said the United States "remains steadfast in its support for the peace process to achieve lasting peace and reconciliation for the people of Northern Ireland".
The veteran Democrat Senator Ted Kennedy, who was strongly critical of republicans over the Belfast murder of Robert McCartney, congratulated Gerry Adams for his role in what was "a watershed in the peace process".
General John de Chastelain will meet a number of politicians
"Hopefully, this dramatic and historic step toward peace will be embraced by the unionist community and become a new dawn for the peace process, so that the all-important restoration of the Northern Ireland Assembly can take place as soon as possible," Mr Kennedy said.
One loyalist spokesman said loyalist paramilitaries would not be following the IRA's decommissioning move.
Sammy Duddy, a member of the Ulster Political Research Group - which advises the UDA, said: "The general has no chance of seeing that achieved. Should he live to be 208, he'll never see it."
Making his report on Monday, General De Chastelain said he had handled every gun and made an inventory of the ordnance, which was in line with estimates provided by the UK and Irish security services.
Two churchmen, one Catholic and one Protestant, witnessed the final acts of the decommissioning process.
Belfast priest Father Alec Reid and ex-Methodist president Rev Harold Good said "beyond any shadow of doubt, the arms of the IRA have now been decommissioned".
However, unionists reacted with scepticism, saying the decommissioning process was not transparent enough without photographic evidence and inventory and details on how the weapons were "put beyond use".
2 tonnes of Semtex
20-30 heavy machine guns
7 Surface-to-air missiles (unused)
7 flame throwers
11 rocket-propelled grenade launchers
90 hand guns
Source: Security estimates/Jane's Intelligence Review
Sinn Fein President Gerry Adams said on Tuesday: "There can be genuine concerns about all of this and people need some time to absorb it.
"But at the end of the day, are they (sceptical unionists) saying that de Chastelain and the other commissioners are liars? Are they saying that Harold Good is a liar, that Fr Alec Reid is a liar?
"Whatever about their views of Sinn Fein - or indeed Mr Blair or the taoiseach (Bertie Ahern) - is that what it amounts to?"
However, DUP MP David Simpson said the facts had to be established "in the cool light of day".
"I have heard what Gerry Adams said about these people being called liars - that is not the case," he said.
"These people were shown a certain amount of arms - they have to take the word of the Provisional IRA."
Ulster Unionist peer Lord Kilclooney said it would be some time before unionists were convinced of the IRA's intentions.
However, the man who helped broker the Good Friday Agreement, Senator George Mitchell, said he believed the events would lead to political progress.