The packed room, including the Queen Consort, the Prince of Wales and Prime Minister Liz Truss, repeated back the phrase.
Making his declaration, the King said it was his "most sorrowful duty" to announce the death of his mother.
"I know how deeply you, the entire nation, and I think I may say the whole world, sympathise with me in the irreparable loss we've all suffered,” he said.
“It is the greatest consolation to me to know the sympathy expressed by so many to my sister and brothers.”
The ceremony was attended by 200 members of the Privy Council. They included former Prime Ministers Boris Johnson, Theresa May, David Cameron, Gordon Brown, Tony Blair and John Major.
King Charles III decided to allow television cameras into the Accession Council for the first time to allow the public to view proceedings.
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