Northern Ireland Secretary Peter Mandelson cited the reaction from David Trimble, leader of the Protestant Ulster Unionist Party, saying its "long standing and proper concerns have now been addressed."
"On the basis of such a positive response to these proposals, not only from his party but all the pro-(Good Friday) Agreement parties, I can confirm to the House that I will bring forward the necessary order to restore the Northern Ireland Assembly and its executive by 22 May," he told parliament.
"I feel hopeful and confident that the ultimate prize -- stable, inclusive government in Northern Ireland and an unbreakable peace -- will at long last be within our grasp."
Mandelson's comments came after the IRA pledged at the weekend to put its arms "completely and verifiably beyond use." The offer breathed new life into the peace process which had been deadlocked over guerrilla disarmament.
Mandelson added that Trimble "has acknowledged the real significance of the IRA statement and the fact that it appears to break new ground."
Britain suspended Belfast's home-rule government of Roman Catholic and Protestant parties in February after just 72 days because it said the IRA had shown no commitment to disarm.
The Northern Ireland Secretary said that proved to be a "bruising" experience for all, but outlined moves to keep the peace process moving amid hopes that a line could be drawn under 30 years of sectarian violence that has cost 3,600 lives.
He said the two international statesmen appointed to supervise IRA weapons dumps would visit the British-ruled province next Monday.
They are the former Finnish President Martti Ahtisaari and former African National Congress (ANC) leader Cyril Ramaphosa.
Earlier Monday, British Prime Minister Tony Blair's spokesman said it was "realistic" to get Northern Ireland's power-sharing government restarted by May 22.
But both Mandelson and Trimble stressed that they must hear from other groups. "It is important that we now hear, in similar terms, from the main loyalist organizations," said Mandelson.
Trimble was encouraged but noted that his party still had to take a final and formal decision on the IRA statement.
"While it does appear to break new ground, there are still matters there that should be probed and until we get sufficiently satisfactory answers on those and related matters as well, it would be premature to make a decision on this matter," he told parliament.
Irish Prime Minister Bertie Ahern told Reuters in Dublin: "As all the parties examine the proposals that Tony Blair and I issued them, no doubt they will have pointof clarification -- already Mr Trimble has stated that he has some."
"There is considerable excitement that the political process is picking up again," Mitchel McLaughlin, chairman of the IRA's political ally Sinn Fein, told reporters in Belfast after meeting members of the party's Assembly team.
The IRA is believed to own 40 rocket-propelled grenade launchers, 650 AK-47 automatic rifles, hundreds of handguns and 32 machineguns, as well as at least two tons of plastic explosive and tons of ammunition.