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The meeting took place at Harry and Meghan's home at Frogmore Cottage in Windsor, according to ABC News' royal contributor Omid Scobie. Charles' wife, Camilla, was not in attendance.
Archie, who was born on May 6, met his aunt and uncle, Prince William and Duchess Kate, earlier this week.
The newest member of the royal family was also introduced to his great-grandparents, Queen Elizabeth II and Philip, the Duke of Edinburgh, last week, on the same day Harry and Meghan announced his name and posed with him in photos.
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The Duke and Duchess of Sussex are pleased to announce they have named their first born child: Archie Harrison Mountbatten-Windsor This afternoon Their Royal Highnesses introduced Her Majesty The Queen to her eighth great-grandchild at Windsor Castle. The Duke of Edinburgh and The Duchess’ mother were also present for this special occasion. Photo credit: Chris Allerton ©️SussexRoyal
ABC News' Katie Kindelan contributed to this report.