The Sinn Fein president, Mr Gerry Adams, said the Provisional IRA's arms initiative was unprecedented in 200 years of "armed struggle". However, he admitted many republicans were concerned about the development.
"This ground-breaking and unprecedented IRA initiative is both courageous and imaginative. In 200 years there has not been an initiative like this," he said.
"It does demonstrate that the IRA leadership is committed to trying to enhance the peace process. Everyone who wants the peace process to work will welcome the announcement."
Mr Adams said his party was having to steady the nerves of grassroots republicans. "Let no one think this has been done without difficulties. Let no one think there are not all sorts of worries opened up within republicanism."
But, he said, many republicans would stay within Sinn Fein and continue to express their concerns from within party structures. Mr Adams dismissed the idea of a similar gesture by loyalist paramilitaries as irrelevant.
"How could they bring inspectors to their arms dumps? What would that prove except that the British government had supplied a lot of their arms? The important thing from the republican and nationalist point of view is that loyalist guns are silent."
Mr Adams said the onus was now on the British government to fulfil its obligations under the Belfast Agreement and to implement radical policing reforms.
The SDLP leader, Mr John Hume, welcomed the IRA initiative as a significant first step. "It is an important first step on the road to complete disarmament. It is our duty to keep making progress and to keep building on it," he said.
The Ulster Unionist Party leader, Mr David Trimble, said he hoped the inspection of Provisional IRA arms dumps by the two international monitors would be followed by other moves towards decommissioning.
The North's First Minister, who is visiting the Middle East, warmly welcomed the inspection, saying: "I think it is good news and I hope that those who doubted whether it would happen will acknowledge that we have made progress."
However, the anti-agreement UUP MP, Mr Jeffrey Donaldson, said it was still not clear if the Provisional IRA really was ready to decommission its weapons. "I have made it clear that the inspection of a few arms dumps does not represent progress itself," he said.
The DUP leader, the Rev Ian Paisley, said the Provisional IRA remained in control of its dumps and for anyone to claim the inspection represented decommissioning was "disgraceful".
His deputy leader, Mr Peter Robinson, said the unionist community would judge the Provisionals not on their arms "gimmick" but on the murder of Mr Ed McCoy in Belfast last month. Mr Norman Boyd of the Northern Ireland Unionist Party said most people in the North viewed the inspection of dumps as meaningless.
The 32 County Sovereignty Movement condemned the Provisional IRA leadership's actions as "surrender". It said it was highly significant that the two arms inspectors reported directly to the British Prime Minister.
The Alliance party welcomed the inspection of the arms dumps. Its leader, Mr Sean Neeson, said:
"This is an unprecedented, historic move by the IRA. This step should inject much needed stability into the peace process and provide a more solid basis for the Assembly to function in." He said loyalists must immediate follow the Provisional IRA's example.
Mr Gary McMichael, of the Ulster Democratic Party, the UDA's political wing, said the inspection of arms dumps was no big surprise.
"This was part of an arrangement to facilitate the renewal of the Stormont Executive and it was fully expected that republicans would keep their word in this regard.
"Loyalists wait with anticipation for the IRA to fulfil its other commitment to actually put its arms beyond use."