The President, Mrs McAleese, gave a simple message to the new ministers in Northern Ireland's Assembly: "You can work with your enemies and gain."
In Aberdeen on the second day of her British tour, the President acknowledged people in Northern Ireland might find some of the Executive's ministers "provocative", but she called on all the people of the North to claim "ownership" of the devolved settlement.
Speaking to The Irish Times yesterday, she quoted her grandmother's advice when it came to coping with difficult situations. "You don't have to like it, you just have to do it," she said, adding the European Union was an example where working together did not reduce sovereignty but enhanced it. She hoped similar could be said of the coalition executive in Belfast.
"Ministers have pledged to work for all the people. They have to be met halfway by the people they are working for. The ministers are quietly working for good government," she said.
She called on people to "ransack the past for good shared memories" and warned you couldn't "chisel away at centuries of hatred and expect hearts to soften over night".
Pointing to the example of the Irish involvement in the first World War, when a quarter of a million men fought for the Allies, she said there were "memories to pull out of the shoe box " which both communities could cherish.
She looked forward to the possibility of hosting a reception for Queen Elizabeth at the Presidential residence in the Phoenix Park, but the final decision lay with the two governments.
The President flies to London today where have lunch with the queen at Buckingham Palace. She will also visit the Irish Centre in Camden and will give a speech at St Paul's Cathedral on the theme of peace in the 21st century.
Mrs McAleese remarked on the benign coincidence that she was visiting Scotland and seeing the queen at a time of such significance in the peace process.
Her remarks came as she accepted an honorary degree from the University of Aberdeen and inaugurated the Research Institute of Irish and Scottish Studies.
The institute is the first in the world to specialise in comparative studies of the two nations. The President said it marked a new era of understanding between Scotland and Ireland.
"These developments reflect a desire to know more about each other, to point the benign light of scholarship at the many past misunderstandings."
Mrs McAleese said the advent of a devolved parliament in Edinburgh and the Assembly in Belfast meant a "restoration of interrupted friendships". She called for a "joyful curiosity, not a morbid one". This theme, of the joint experience of Scots and Irish being used to heal the wounds in Northern Ireland, is central to the President's five-day tour of Scotland and England.
The institute has been set up with a strong academic base. Lead by the noted Scottish historian, Mr Tom Devine, a third generation Irish-Scot, it boasts an advisory board, including Seamus Heaney, Seamus Deane, Roy Foster, Cathal O Hainle and Ms Helen Vendler, of Harvard University. It plans to build on the Irish-Scottish academic initiative that links Trinity College, Dublin, with Strathclyde and Aberdeen universities.
The President's visit to Scotland began in a formal and sombre mood. Yesterday that lightened as the opening ceremony for the institute celebrated the ancient culture of Scotland and Ireland through musical recitals and poetry.
Amid this atmosphere of mutual understanding, the President jokingly hit upon the one possible strand of dispute. "I had to come to Scotland to hear St Patrick described as a Scottish saint. There's a fair bit of jockeying for position here," she said.