Boris Johnson could be out of Downing Street with a new prime minister in place by the middle of September, a minister has said.
Johnson announced his resignation last week, saying he would remain in place until a new Conservative Party leader had been elected.
Some 11 Tory MPs have so far put themselves forward to become the Tory party leader and PM.
George Eustice said Johnson was “right” to continue in a caretaker capacity in the face of calls for him to leave sooner.
The environment secretary said: “That’s what Theresa May did. That’s what David Cameron did. It’s what Tony Blair did. It’s what happens in these situations."
Watch: Eleven Conservatives now bidding to be next prime minister
The 1922 committee of Tory backbenchers, which is responsible for setting the rules in any Conservative Party leadership contest, will take action on Monday to speed up the process of appointing Johnson's successor.
A vote is taking place on Monday afternoon for the new executive of the committee, which will then meet immediately after to decide the rules and procedure for the contest.
It is expected the 1922 Committee will raise the nominations threshold from 10% of Tory MPs to 20% in order to narrow the initial pool of contenders.
The chair of the committee, Sir Graham Brady, will meet with the Tory party board to sign off the timetable, with an announcement expected at about 7pm.
Conservative MPs will start voting on their next leader this week, with a view to whittling it down to two before the parliamentary summer recess in two weeks' times.
The final two candidates will then take part in a series of hustings and events around the country in a bid to win the votes of Conservative Party members, who have the final say.
Eustice told Sky News: "We'll be down to probably just two candidates by the end of next week.
"And those two candidates will go out on a series of hustings around the country during August, possibly early September as well.
"I would imagine at some time in the middle of September, perhaps we'll have a new leader in place. "
In his resignation speech outside Downing Street, Johnson said that he had agreed with Sir Graham “that the process of choosing that new leader should begin now and the timetable will be announced next week”.
Liz Truss became the latest contender to throw her hat into the ring on Sunday, insisting she can be "trusted to deliver".
The newly appointed Foreign Office minister Rehman Chishti announced his candidacy on Sunday, meaning there are now 11 Tories in the running for the top job.
Other contenders include former health secretaries Sajid Javid and Jeremy Hunt, ex-chancellor Rishi Sunak, his successor Nadhim Zahawi, Transport Secretary Grant Shapps and trade minister Penny Mordaunt.
Former minister Kemi Badenoch and senior backbencher Tom Tugendhat have also announced the are vying to become prime minister.