The new prime minister will be in place before the fiscal statement on October 31, Sir Graham Brady, the chairman of the 1922 Committee of backbench Tory MPs, said.
Liz Truss has announced her resignation after a chaotic 44 days in office during which she lost the confidence of Tory MPs and the public and oversaw economic turbulence.
She is set to become the shortest serving Prime Minister in history after she battled an open revolt from Conservatives demanding her departure.
Speaking from a lectern in Downing Street, Ms Truss said she had told the King she was resigning as the leader of the Conservative Party as she recognised she “cannot deliver the mandate” which Tory members gave her little over six weeks ago.
She held talks with the chairman of the 1922 Committee of backbench Conservatives Sir Graham Brady and agreed to a fresh leadership election “to be completed within the next week”.
“This will ensure that we remain on a path to deliver our fiscal plan and maintain our country’s economic stability and national security,” she added, as she was accompanied by husband Hugh O’Leary.
“I will remain as Prime Minister until a successor has been chosen.”
Labour leader Sir Keir Starmer demanded a general election “now” so that the nation can have “a chance at a fresh start”.
Without a general election, the Conservatives will be on their third prime minister on the mandate won by Boris Johnson in December 2019.
Sir Keir said: “The Conservative Party has shown it no longer has a mandate to govern.
“The British public deserve a proper say on the country’s future. They must have the chance to compare the Tories’ chaos with Labour’s plans to sort out their mess, grow the economy for working people and rebuild the country for a fairer, greener future.
“We must have a chance at a fresh start. We need a general election – now.”
Ms Truss’s resignation came just a little over 24 hours after she told MPs she was “a fighter, not a quitter”.
But her odds of survival were slashed after chaotic scenes in the Commons followed the resignation of Suella Braverman as home secretary.
The number of Tory MPs publicly demanding Ms Truss’s resignation doubled before lunch was over on Thursday, taking the total to 15, but a far greater number were privately agitating for her exit.
The mechanism of how the next leader – and Prime Minister – will be chosen was unclear.
Allies of Jeremy Hunt, the new Chancellor brought in to shore up the economy and Ms Truss’s premiership after chaos on the financial markets, said he would not be standing.
The pound lifted on the resignation announcement following another volatile 24 hours for the currency amid political turmoil.
Liberal Democrat leader Sir Ed Davey said: “We don’t need another Conservative Prime Minister lurching from crisis to crisis.
“We need a General Election now and the Conservatives out of power.”
Ms Truss had summoned Sir Graham to Downing Street for a hastily-arranged meeting on Thursday morning, with sources saying she was “taking the temperature” of the Tory party.
What Sir Graham told her was unclear, but she was left realising her time was up. “The statement was the result” of their conversations, a source confirmed.
Ms Truss’s 44 days in office falls months behind the next shortest premiership of Tory statesman George Canning, who spent 118 full days as PM in 1827 before dying in office.
