Charles has told Liz Truss that the death of his mother was “the moment I have been dreading”.
The Prime Minister had her first audience with the new King following his return to Buckingham Palace from Balmoral.
Ms Truss, who only took office this week, curtsied as she was shown in to meet Charles for the first of what will be 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, Ms Truss led tributes in the House of Commons to the Queen as she urged the country to support their new monarch.
She told MPs the King “bears an awesome responsibility that he now carries for all of us”, adding: “Even as he mourns, his sense of duty and service is clear.”
She said the British people, the Commonwealth and all MPs must support Charles as he takes the country forward to a “new era of hope and progress, our new Carolean age”.
While “our lives changed forever” with the death of the Queen, she said Britons must show the world “we do not fear what lies ahead”.
On Tuesday, Ms Truss met the Queen at her Scottish estate when she was invited to form a Government following her victory in the Conservative leadership contest.
On Saturday, she will attend the Accession Council in the State Apartments of St James’s Palace where Charles will be formally proclaimed King.