Senior ministers will attend the Accession Council at St James’s Palace where Charles will be formally proclaimed sovereign.
They will later travel to Buckingham Palace for an audience with the monarch.
Ms Truss, who was invited to form a Government by the late Queen on Tuesday, had her initial audience with the King on Friday.
The Prime Minister curtsied as she was ushered in by a Palace aide for the first of what will be their regular weekly encounters.
As she offered her condolences, the King shook her hand and thanked her, saying: “You are very kind for coming – I know how busy you are.”
He added: “But it’s been so touching this afternoon when we arrived here, all those people come to give their condolences.”
Ms Truss again repeated: “Your Majesty, my very greatest sympathies.”
He replied: “You are very kind. It was the moment I have been dreading, as I know a lot of people have.
"We’ll try to keep everything going. Come, come have a seat.”
Earlier, the Prime Minister led tributes in the House of Commons to the Queen as she urged the country to support their new monarch.
Those tributes will continue during rare Saturday sittings of both the Commons and the House of Lords.
Proceedings in the lower chamber will begin at 1pm with a small number of senior MPs taking an oath of allegiance to the King, and are expect to continue to around 10pm.
King Charles III addressing his peopleYui Mok
Prime Minister Liz Truss met with King Charles III on FridayYui Mok