Liz Truss has resigned as prime minister after 45 days in office marked by turmoil, triggering the second Tory leadership election in four months.
Ms Truss said her successor would be elected by next week after a rebellion by Tory MPs forced her to quit.
Boris Johnson is among MPs said to be considering bids but Chancellor Jeremy Hunt has ruled himself out.
Tory MPs revolted against Ms Truss after a series of U-turns on her economic plan sapped her of authority.
In a brief speech outside Downing Street, Ms Truss said the Conservative Party had elected her on a mandate to cut taxes and boost economic growth.
But given the situation, Ms Truss said: “I recognise that I cannot deliver the mandate on which I was elected by the Conservative Party.”
Labour leader Sir Keir Starmer and other opposition parties called for an immediate general election following Ms Truss’s resignation speech.
Ms Truss said she would remain in post until a successor formally takes over as party leader and is appointed prime minister by King Charles.
While Mr Hunt – who was appointed chancellor last week – will not challenge for the leadership, none of the candidates who stood against Ms Truss in the previous contest have indicated whether they would stand.
However, Conservative sources have told the BBC that Business Secretary Jacob Rees-Mogg has been encouraging colleagues to back Mr Johnson in the race.
Sir Graham Brady, the chairman of the 1922 committee of backbench Conservative MPs, said a new leader could be chosen by next Friday.
Under party rules, leadership hopefuls will need to secure the support of 100 MPs in order to enter the contest – this means a maximum of three candidates can stand.
A first ballot will be held among MPs and the person with the lowest number of votes will be eliminated, if there are three candidates.
If a second ballot is needed, MPs will be able to signal who they prefer through an indicative vote.
And if both candidates opt to stay in the race, the final decision will go to party members via an online vote.
Ms Truss will become the shortest-serving PM in British history when she stands down.