Photo: Alberto Pezzali/AP/Shutterstock

Mandatory Credit: Photo by Alberto Pezzali/AP/Shutterstock (13381171b) Britain’s Prince William and Kate, Princess of Wales, left, and Britain’s Prince Harry and Meghan, Duchess of Sussex walk to greet the crowds after viewing the floral tributes for the late Queen Elizabeth II outside Windsor Castle, in Windsor, England Royals, Windsor, United Kingdom - 10 Sep 2022

William thought the walkabout to greet the crowds “was an important show of unity at an incredibly difficult time for the family,” a royal source says.

For more on Queen Elizabeth, listen below to our daily podcast PEOPLE Every Day.

Another source adds that security was not expecting both couples at the walkabout.

A palace insider tells PEOPLE: “It’s such an extraordinary historical moment and also a deeply personal one for the family that you’d hope and think that all members of the family would unite and support [the King] especially. And perhaps some of those wounds can be healed in the process.”

The couples delighted the crowds of people, who have flocked to the castle since news of theQueen’s deathwas announced on Thursday.

Alberto Pezzali/AP/Shutterstock

Mandatory Credit: Photo by Alberto Pezzali/AP/Shutterstock (13381171d) Britain’s Prince William and Kate, Princess of Wales, left, and Britain’s Prince Harry and Meghan, Duchess of Sussex walk to greet the crowds after viewing the floral tributes for the late Queen Elizabeth II outside Windsor Castle, in Windsor, England Royals, Windsor, United Kingdom - 10 Sep 2022

Kate and William, 40, recently moved to Windsor, making them a short distance from Harry and Meghan’s U.K. home, Frogmore Cottage, which is on the Queen’s Windsor Castle estate. Meghan, 41, and Harry, 37, who moved to California in 2020, are expected to remain in the U.K. until theQueen’s funeral, which will take place on Sept. 19.

It was the second outing for William on Saturday. Earlier in the day, he witnessedthe solemn historicalmoment that saw his fatherKing Charles IIIofficially proclaimed monarch at St. James’s Palace in London.

Can’t get enough ofPEOPLE’s Royals coverage?Sign up for our free Royals newsletterto get the latest updates onKate Middleton,Meghan Markleand more!

During the Accession Council of the Privy Council (comprising senior Cabinet ministers, judges and leaders of the Church of England) at St. James’s Palace, it was proclaimed that “The crown of the United Kingdom of Great Britain and Northern Ireland is solely and rightfully come to thePrince CharlesPhilip Arthur George.”

Prince William and Prince Harry.James Whatling / MEGA

The Prince and Princess of Wales view the tributes at Windsor

On Wednesday, the couple took their three children,Prince George, 9,Princess Charlotte, 7, andPrince Louis, 4, totheir new school, Lambrook, after the family moved into Adelaide Cottage.

King Charles also acknowledged his younger son, who is now fifth in line to the throne, in the speech.

“I want also to express my love for Harry and Meghan as they continue to build their lives overseas,” he said.

Meghan Markle and Prince Harry.Alberto Pezzali/AP/Shutterstock

Mandatory Credit: Photo by Alberto Pezzali/AP/Shutterstock (13381171a) Britain’s Prince Harry and Meghan, Duchess of Sussex view the floral tributes for the late Queen Elizabeth II outside Windsor Castle, in Windsor, England Royals, Windsor, United Kingdom - 10 Sep 2022

As news of concerns for the Queen’s health broke on Thursday, William immediately made preparations to fly to Scotland alongside his uncles,Prince AndrewandPrince Edward, and Edward’s wifeSophie, Countess of Wessex.Prince Harryalso made his way to Scotland, having been in Europe for a scheduled appearance in London that day. But they weren’t able to get to the Queen’s bedside before she died.

“The Queen died peacefully at Balmoral this afternoon,” Buckingham Palace announced inan official statementon Thursday.

The statement continued, “The King and The Queen Consort will remain at Balmoral this evening and will return to London tomorrow.”

James Whatling / MEGA

The Prince and Princess of Wales view the tributes left after the Death of Queen Elizabeth II, at Windsor Castle, Windsor, Berkshire, UK, on the 10th September 2022. 10 Sep 2022 Pictured: The Prince and Princess of Wales view the tributes left after the Death of Queen Elizabeth II, at Windsor Castle, Windsor, Berkshire, UK, on the 10th September 2022. Photo credit: James Whatling / MEGA TheMegaAgency.com +1 888 505 6342

In anofficial statementreleased Saturday, William said, “On Thursday, the world lost an extraordinary leader, whose commitment to the country, the Realms and the Commonwealth was absolute. So much will be said in the days ahead about the meaning of her historic reign.”

“I, however, have lost a grandmother,” he continued, reflecting on what the Queen meant to his family. “And while I will grieve her loss, I also feel incredibly grateful. I have had the benefit of The Queen’s wisdom and reassurance into my fifth decade. My wife has had twenty years of her guidance and support. My three children have got to spend holidays with her and create memories that will last their whole lives.”

From left: Prince George, Kate Middleton, Prince Louis, Prince William and Princess Charlotte.PA

Prince George, Princess Charlotte and Prince Louis, accompanied by their parents the Duke and Duchess of Cambridge, arrive for a settling in afternoon at Lambrook School, near Ascot in Berkshire

Hewent on to thank the late Queen"for the kindness she showed my family and me. And I thank her on behalf of my generation for providing an example of service and dignity in public life that was from a different age, but always relevant to us all."

source: people.com