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The referendum, held yesterday on both sides of the border, returned a resounding "yes" vote with 71% of voters from Northern Ireland and 94% of those in the Irish Republic showing their support for the Good Friday peace agreement.
"This is the result we have worked for and wanted," said Mr Blair. "It's another giant stride along the path to peace, hope and the future."
The agreement signed last Easter seeks to resolve relationships within Northern Ireland - between Northern Ireland and the Republic and between both parts of Ireland and England, Scotland and Wales - and pave the way for devolution from Westminster with a new all-inclusive Assembly.
It was signed on 10 April - Good Friday - by all interested parties except Rev Dr Ian Paisley's Democratic Unionist Party and Bob McCartney's United Kingdom Unionist Party. They objected to the presence of the IRA's political wing Sinn Fein in the multi-party talks leading up to the agreement.
The Northern Ireland Secretary, Mo Mowlam, told reporters she was delighted with the two nations' endorsement of the agreement.
"An important step forward"
Ulster Unionist Party leader David Trimble said: "It is quite clear that a majority of unionists - not as big a majority of unionists as I would have liked - but a clear majority - have endorsed this agreement. We have taken an important step forward."
John Hume, leader of the nationalist SDLP, said that for the first time the people of both sides of the Irish border were speaking as one.
Sinn Fein leader Gerry Adams said he was prepared to sit down with David Trimble in a new Northern Ireland assembly "now".
Irish Prime Minister Bertie Ahern said the overwhelming result was the true "voice of the people".
The British Government will press ahead next month with elections for a Northern Ireland Assembly.
After the euphoria of the positive vote for a peaceful solution to the problems of Northern Ireland came the reality.
The first three years of the agreement's implementation saw accusations and counter-accusation from both sides of the divide.
Unionists said the republicans had not complied with the spirit of the agreement's requirement for the decommissioning of arms.
And Sinn Fein accused the British government of failing to demilitarise quickly enough. It added that it could not force anyone to give up arms and that the agreement only stated that the parties should use all their power to influence the process.
Disagreement over decommissioning and policing led to the suspension of the Northern Ireland Assembly twice in 18 months - in February-May 2000 and in August 2001.
The issue has remained the major stumbling block in talks between all parties seeking to restore devolution since the Northern Ireland Assembly was suspended in October 2002 over alleged intelligence gathering by republicans.
Direct rule finally ended in May 2007 when the Northern Ireland Assembly met with the return of devolution and DUP leader Ian Paisley as first minister.
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