The Queen and the Pope have each been separately acknowledging the return of devolution to Northern Ireland.
Her Majesty thanked President Bush for US efforts, whilst the Vatican's British and Irish ambassadors are due to have an audience with the Pope.
NI Secretary Peter Hain said the new executive was the resolution of what had been the most "intractable source of political conflict in Europe."
The comments come as new ministers carry out their first engagements.
The Queen spoke about the political situation in Northern Ireland during a dinner at the British Ambassador's residence in Washington at the end of her six-day state visit.
She said: "I would like to take this opportunity, on the day that has seen the formal transfer of power to the... Northern Ireland Government, to thank you and your predecessors for your contribution to bringing peace in Northern Ireland."
Pope Benedict is also expected to congratulate the governments for their work to help restore devolution.
He has extended a personal invitation to the British Ambassador to the Holy See, Francis Campbell, and his Irish counterpart Philip McDonagh.
Both men are from Northern Ireland and have worked on the peace process in the past.
They will attend a traditional farewell gathering at the Vatican before the Pope leaves for Sau Paulo in Brazil.
At Stormont, First and Deputy First Ministers Ian Paisley and Martin McGuinness are hosting their first joint reception, welcoming ethnic group representatives.
A slimmed-down Northern Ireland Office team is also focussing on its remaining responsibilities, such as security.
The new ministers are getting to grips with their roles, with new Regional Development Minister Conor Murphy already confirming investment of more than £14m in roads around Banbridge.
Among those out on the road are education minister Catriona Ruane of Sinn Fein, who is touring two schools, and social development minister Margaret Ritchie of the SDLP, who visits a Belfast building site.
The first round-table meeting of the new executive is due to take place on Thursday.
An unprecedented meeting in March between Mr Paisley and Sinn Fein leader Gerry Adams set the scene for Tuesday's historic ceremony at Stormont, when power-sharing was restored.
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