President Clinton has assured the President, Mrs McAleese, of his continuing commitment to the Northern Ireland peace process and said he is "very anxious" to pay a second visit to Ireland at the first available opportunity.
President McAleese emerged from a 30-minute meeting in the Oval Office of the White House almost awe-struck by the extent of Mr Clinton's knowledge of the situation in Northern Ireland in the last days before the Assembly election.
"He shows a very shrewd understanding of where we are up to in the peace process . . . He is keeping his finger very much on the pulse of what is going on."
President McAleese told reporters that her first visit to Washington as President was an opportunity "to say thank you to him on behalf of the Irish people for all he has done to bring about a situation where we can look forward now to an entirely new future for our children, a future based on partnership and peace".
On a day when the White House is focusing almost completely on President Clinton's visit to China, the Irish group was jubilant at the attention he was willing to give to President McAleese.
Also at the meeting, which lasted twice the allotted time, were the Secretary of State, Ms Madeleine Albright; the National Security Adviser, Mr Sandy Berger; the President's chief-of-staff, Mr Erskine Bowles; and Vice-President Gore's security adviser, Mr Leon Fuerth.
On the Irish side were the Minister for Foreign Affairs, Mr Andrews, the Irish Ambassador, Mr Sean O hUiginn, and the head of the Anglo-Irish section, Mr Dermot Gallagher.
President McAleese later described the meeting as "very, very comfortable, very relaxed, and we shared a few jokes". Mr Clinton told Mr Andrews that he would like to come to Ireland "every month" if he could.
Referring to the planned trip of Mrs Hillary Clinton to Northern Ireland in the autumn for a women's conference, Mr Clinton said that this would not be a good time for him to go as Congress would be coming back from its summer break.
Back at her hotel later, President McAleese expanded on her impressions of the meeting. It was her third time to meet President Clinton, "not that he would remember me out of the hundreds of thousands of people he has met".
She said he was interested in her views on the peace process and they discussed "where we thought the election would take us to and the unfolding of the process beyond that and how quickly would we bed down with the certainty that peace was sustainable".
Asked if the President was apprehensive about how the process would work, President McAleese said: "No more apprehensive than we would be. We all know how there are certain forces of darkness that would like to draw the people of Northern Ireland and Ireland generally down into the vortex where we have come from. We have all been there and we all know what a wasteland that is".
Saying that the people had given an emphatic answer in the referendums, the President said it was important now that the people had leaders like President Clinton who were prepared to take risks.
Later President McAleese went to the Supreme Court where she had lunch with the Chief Justice, Mr William Rehnquist.
In the afternoon she went to Georgetown University where she was awarded the President's Medal by its president, Father Leo O'Donovan SJ.
In a lengthy address, Mrs McAleese described the changes affecting modern Ireland, economically and culturally. She also described the Belfast Agreement as "an unprecedented and collective act of will by key political leaders to learn and apply the lesson of Irish history".
The dinner in her honour at the Irish Embassy last night included the Commerce Secretary, Mr William Daley, and the Education Secretary, Mr Richard Riley. Also invited were eight members of Congress, including Senator Edward Kennedy.