The Duke and Duchess of Cambridge discussed the implications of Brexit with President Michael D Higgins during the first day of their Irish tour.
Prince William and Kate Middleton talked about the UK’s decision to leave the EU during a meeting with the President his wife Sabina.
They also spoke about building on the foundations of the Good Friday Agreement which ushered in peace in Northern Ireland, said a spokesman for the president.
During a visit to Dublin’s Garden of Remembrance, the couple called for a “brighter future” in a handwritten note left with a wreath.
The couple also met Taoiseach Leo Varadkar and his partner Matt Barrett at Government Buildings.
The visitors were given a brief tour of the building en route to Mr Varadkar’s office, where they sat for a lengthy conversation.
The couple then signed he visitor’s book, as Prince William’s brother, Harry, and his wife Meghan Markle had done in 2018.
Mr Varadkar translated from the Irish saying that it required the Duke to write his name and address. “Would you like an address?” asked the Duke.
To which Mr Varadkar replied: “What’s the postcode for Kensington Palace.”
The royal couple arrived in Dublin on Tuesday morning, beginning a three-day visit to Ireland, their first official visit here.
They arrived at the President’s residence in the Phoenix Park shortly after 2.15pm where they were announced into the State Reception Room by the aide-de-camp to the President.
The Duke and Duchess last met the President during the commemorations that marked the centenary of the start of the first World War in June 2014.
The Duchess of Cambridge was wearing a coat designed by the London-based French designer, Catherine Walker. She wore a vivid green dress designed by the London-based Italian designer, Alessandra Rich, and also a black velvet hair band.
The couple signed the distinguished visitors’ book before they entered the State drawing room and the President’s study for what was described as a “short tete-a-tete”.
The party then proceed to the drawing room for a bilateral meeting. Accompanying the President was his secretary-general, Art O'Leary; the Irish Ambassador to the United Kingdom, Adrian O'Neill, and the president's adviser Claire Power.
The couple were accompanied by Robin Barnett, British ambassador to Ireland, and Simon Case, who is private secretary to Prince William.
The Duke and Duchess flew to Dublin Airport on a commercial Aer Lingus flight and were greeted by a small group of dignitaries led by Mr Barnett.
Following the meeting at the Áras, the Duke and Duchess went to the South Portico where they rang the Peace Bell. The bell, which dates from the 19th century, was introduced to the Áras in 2009 by former president Mary McAleese to mark the 10th anniversary of the Belfast Agreement.
The couple departed Áras an Uachtaráin for the Garden of Remembrance, where they will follow in the footsteps of Queen Elizabeth, who laid a wreath in 2011 at the memorial to those who died for Irish freedom over the centuries.
In a statement before their arrival, the couple said they hoped the visit would “build on the theme of remembrance and reconciliation” which followed on from the queen’s visit.
In 2011, the queen visited both the Garden of Remembrance in Parnell Square and the Irish National War Memorial Gardens in Islandbridge where she paid tribute to the Irish who died serving the British crown in two World Wars.
It also follows on from Prince Charles's visit to Mullaghmore in 2015 where he visited the site where his granduncle Lord Mountbatten was killed by the IRA in 1979.
The Duke and Duchess said they hoped to build a “lasting friendship with the Irish people”.
They added that they “will learn about local organisations working to support and empower young people and projects which provide opportunities to help them develop important life skills”.
After the meeting at Áras an Uachtaráin, a spokesman for Mr Higgins confirmed Brexit was among the topics of conversation.
He said: “The couples discussed the close ties between the people of Ireland and Britain and the importance of continuing and deepening close relations between all of the peoples of these islands.
“President Higgins, Sabina and their royal highnesses spoke of the challenges ahead, including the implications of the UK’s departure from the European Union and the importance of continuing to build on the foundations of the Good Friday Agreement.
“They also discussed the global challenges of climate change and biodiversity loss and the urgent need to revisit the fundamentals of how we organise our economies and societies if we are to tackle these existential threats in a meaningful way.
“The importance of removing obstacles that inhibit young people from building their skills and realising their aspirations for a truly fair and sustainable world, and the particular importance of responding to the vulnerabilities of young people, was among the other topics discussed.”
The Duke and Duchess of Cambridge ended the first day of their visit at a reception at the Guinness Storehouse.
The couple, who arrived at about 7.30pm, were greeted at the Guinness gates by John Kennedy, president of Diageo Europe, Turkey and India and Paul Carty, managing director of the storehouse.
The pair then attended a reception in the Gravity Bar, on the top floor of the tourist attraction, which was hosted by Mr Barnett.
Guests on the night included actors Liam Cunningham, Deirdre O’Kane and Robert Sheehan.
Activist Sinéad Burke was also in attendance, alongside rugby player Garry Ringrose and TV presenter Ryan Tubridy.
They also enjoyed a pint of the Black stuff alongside Ireland international rugby player Sene Naoupu.
During a speech to the attendees, Prince William said the relationship between Ireland and UK was very important.
“Catherine and I are delighted to be here tonight,” he said. “Ireland is a country that we have both heard so much about, so we are really excited to be here with you to see it first-hand for ourselves.”
“On a slightly more serious note, I just wanted to thank you all in the room for coming here this evening.
“Thank you for all that you do to support the very special relationship between our two countries. It has been a pleasure to meet so many of you this evening who demonstrate the breadth of our connections across the arts, sports, uniformed services, education, research, and charity sectors.”
He said they valued the friendship between the two countries, and were “committed to strengthening it further”.
He concluded his speech by raising his pint of Guinness and saying “Sláinte”.