In a read-out of the call, a Kensington Palace statement said: “HRH thanked the First Minister for his fitting tribute, on behalf of the people of Wales, to Her Majesty The Queen.
“HRH expressed his and The Princess of Wales’s honour in being asked by His Majesty The King to serve the Welsh people. They will do so with humility and great respect.”
The couple have a “deep affection for Wales,” said the statement, having made their first family home in Anglesey, including during the earliest months of Prince George’s life.
“The Prince and Princess will spend the months and years ahead deepening their relationship with communities across Wales,” the statement added.
“They want to do their part to support the aspirations of the Welsh people and to shine a spotlight on both the challenges and opportunities in front of them.
“The Prince and Princess look forward to celebrating Wales’s proud history and traditions as well as a future that is full of promise.
“They will seek to live up to the proud contribution that members of the Royal family have made in years past.”
It came as thousands of people gathered at Cardiff Castle to hear Charles be proclaimed King in Wales, alongside similar proclamations in Edinburgh and Belfast.
King Charles III and his Queen Consort Camilla will hear condolences from the four home nations in a tour in the coming days ahead of the late Queen’s funeral.
Charles will visit Edinburgh, Belfast and Wales Camilla, and Prime Minister Liz Truss, to hear condolences from politicians and respond to their words of sympathy.
The King will begin his visit to legislators at London’s Westminster Hall on Monday, where both Houses of Parliament will express their condolences to the new monarch and his wife and the King will give his reply.
Later that day, Charles and Camilla will fly to Edinburgh where the King will inspect the Guard of Honour at the Palace of Holyroodhouse, before attending the ceremony of the Keys on the forecourt.
The King will join his other siblings, Andrew, the Duke of York, Edward, the Earl of Wessex, Anne, the Princess Royal and her husband Vice Admiral Sir Tim Laurence in walking behind the Queen’s coffin when it is moved from the Palace of Holyroodhouse.
It will be taken to St Giles’ Cathedral where it will lie for 24 hours so the public can pay their respects.