The King has met with the Prime Minister after greeting crowds of well-wishers outside Palace gates.
It came as thousands of mourners for Queen Elizabeth II had congregated in central London.
And the new monarch was met with cheers from the crowd as the King’s state Bentley arrived at the gates of the Palace.
The King shook hands with countless members of the public lined up behind a barrier, thanking them for their good wishes.
King Charles III and Queen Consort Camilla
HENRY NICHOLLS
Speaking to Ms Truss, the King said: "It has been so touching this afternoon when we arrived here. All those people come to give their condolences, put flowers... you're very kind.
King Charles III shakes hands with Prime Minister Liz Truss during their first audience at Buckingham Palace
Yui Mok
"The moment I've been dreading, as I know a lot of people have but... try and keep everything going.
Speaking on Thursday, King Charles said he was "mourning profoundly" after the death of his mother.
He said: “We mourn profoundly the passing of a cherished sovereign and a much-loved Mother.
"I know her loss will be deeply felt throughout the country, the Realms and the Commonwealth, and by countless people around the world.”
The new King will be formally proclaimed monarch at a historic Accession Council in the State Apartments of St James’s Palace at 10am on Saturday.
A Principal Proclamation will be read in public for the first time by the Garter King of Arms in the open air from the balcony overlooking Friary Court at St James’s an hour later at 11am.
It will be followed by a flurry of Proclamations around the country, with the second one at City of London at the Royal Exchange at midday on Saturday, and further Proclamations in Scotland, Northern Ireland and Wales at midday on Sunday.