It is the first response from the UK Government to the IRA announcement, which has breathed new life into the peace process.
Three security installations are being demolished in south Armagh while an army base in Magherafelt, County Londonderry, is to be dismantled.
Northern Ireland Secretary John Reid is expected to outline further measures, including a reduction in troop levels, in the House of Commons on Wednesday afternoon.
Demilitarisation was a key demand from Sinn Fein during discussions before the breakthrough.
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On Wednesday, the prime minister's official spokesman said the four security installations would be dismantled "logistically and physically as quickly as possible".
He also indicated a reduction in 13,000 troops currently based in Northern Ireland "when the threat-level" allows.
"We don't want to keep them higher than they need in any normal security situation," he said.
Demilitarisation
Dr Reid has already promised a generous response to what he said was the IRA's "historic and unprecedented" decision.
"It means, secondly, we can implement the Agreement in all of its aspects.
"And it means we can respond both in the short term and hopefully plan for the longer term on a demilitarisation, a normalisation of Northern
Ireland society," Dr Reid said on Wednesday morning.
Unionist response
A few hours later, the Ulster Unionist leader David Trimble, who withdrew his three ministers from the power-sharing executive last week, announced that he had renominated them to their departments of government at Stormont.
He had to do this before midnight on Thursday to avoid suspension of the devolved administration.
He has called a meeting of his party's ruling executive on Saturday to ask it to approve the reconstituting of the executive.
He needs the backing of the executive to ensure his move back into government with republicans is party policy, forcing critics of the policy to fall into line.
Meanwhile, Lagan Valley Ulster Unionist MP Jeffrey Donaldson said the party should retain the option to leave government again if there were no further IRA moves on arms.
Democratic Unionist Party deputy leader Peter Robinson has criticised David Trimble's proposed move back into government.
"It is only when you know what has been put out of use that you can make a proper judgement," he said.
Logjam
Sinn Fein leader Gerry Adams has said the issue of arms should now be left with General John de Chastelain's international decommissioning body.
Mr Adams said Tuesday's move by the IRA should now leave the way clear for the political impasse to be broken and real progress to be made.
"We got this initiative because the IRA wanted to save the process despite the way it was being handled," he said.
The international body charged with dealing with paramilitary weapons confirmed on Tuesday that it had witnessed the IRA put a quantity of arms beyond use which it described as "significant".
The material included arms, ammunition and explosives, it said.
Confirming its move, the IRA described its decision as an "unprecedented" decision to save the peace process and a demonstration to others of its genuine intentions.
He said the IRA's move would mean "we can get stability into the political institutions".
Related to this story:
Tony Blair's statement in full
(23 Oct 01 | Northern Ireland)
US congratulates IRA on 'historic' decision
(24 Oct 01 | Northern Ireland)
Bush welcomes IRA arms move
(24 Oct 01 | Northern Ireland)
World press review
(24 Oct 01 | World)
Trimble's ministers to return
(24 Oct 01 | Northern Ireland)
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