Liz Truss will visit the devolved nations with King Charles this week as the monarch leads the UK through a period of national mourning.
While King Charles and Ms Truss, who only gained the keys to Number 10 on Tuesday, will be attending the same "services of reflection", Number 10 said the PM was not accompanying the monarch.
"It's not a requirement, but the prime minister believes it's important to be present for what is a significant moment of national mourning around the United Kingdom," the spokesperson said.
On Friday, the monarch welcomed Ms Truss to the first of what will be their weekly meetings.
During the audience, the King told Ms Truss the death of the Queen was a moment he had "been dreading".
Ms Truss also offered her condolences.
King Charles, accompanied by The Queen Consort, will attend parliament on Monday morning to receive addresses from both the House of Commons and House of Lords.
They will then travel to Edinburgh to join a procession from Holyroodhouse to St Giles' Cathedral.
The procession will leave at 2.35pm, with the King and some members of the Royal Family following on foot.
At 2.55pm, the coffin will be carried into the cathedral with the Crown of Scotland on top, where it will be left to rest until Tuesday.
Last Tuesday, Ms Truss travelled to Balmoral to meet the Queen, who officially appointed her as prime minister and then asked her to form a government.
The picture of the two meeting showed the Queen's last public appearance.
Just 48 hours later, Ms Truss gave a speech on the steps of Downing Street to mark the Queen's death and offered her support to the King.
MPs paid tribute to the Queen with speeches in the Commons on Friday.
Boris Johnson made his first appearance since stepping down as prime minister, asking the public to "think what we asked of her and think what she gave".
The tributes continued in a rare Saturday Commons sitting, where senior MPs also pledged their allegiance to King Charles III.
It was only the sixth time that the Commons has sat on a Saturday since the Second World War.
The other times were:
• 2 September 1939 - for the outbreak of the Second World War
• 30 July 1949 - for summer adjournment debates
• 3 November 1956 - to discuss the Suez Crisis
• 3 April 1982 - to discuss the Falkland Islands invasion
• 19 October 2019 - to discuss Boris Johnson's Brexit deal
Parliament's tributes followed an outpouring of grief from across the political spectrum as the world digested news of the Queen's death at the age of 96.