Housing minister Kit Malthouse has withdrawn from the Tory leadership race as the party considered rules to make it harder for outsiders to stand.
The field of candidates is now down to 11 after James Cleverly also pulled out of the contest.
Mr Malthouse said he was a “realist” and acknowledged there was an “appetite for this contest to be over quickly”.
The executive of the backbench 1922 Committee met to decide the rules for the leadership contest to deal with the crowded field.
Changes are expected to include making candidates secure more nominations to enter the race.
They will also have to clear a higher hurdle to stay in the contest once MPs begin the process of voting, to speed up the process of whittling the contenders down to the final two.
The winner – and the next prime minister – will be decided by Tory members.
Mr Malthouse said: “When I announced my intention to seek the leadership of the Conservative Party, I did so believing that I could make a real difference in delivering a Brexit that would command the support of the House of Commons.
“After 20 years in frontline politics as a councillor, deputy mayor, MP and minister, I also wanted to lead a new generation of Conservatives stepping forward at a time of profound change in our country.
“But that experience has also made me a realist and the last few days have demonstrated that there is an appetite for this contest to be over quickly and for the nation to have a new leader in place as soon as possible.
“As such, it seems right to me that I withdraw my candidature and wish those remaining the very best, always recognising there are going to be very challenging times ahead.”
Earlier on Tuesday, Brexit minister Mr Cleverly said he had withdrawn because his fellow MPs were not comfortable with the idea of picking a “relatively new” colleague.
The MP for Braintree, first elected in 2015, concluded he was “highly unlikely” to reach the final two candidates chosen by MPs.
Senior Tories are keen to set out rules for the contest which will quickly narrow the field down to serious contenders to replace Theresa May, who will quit as party leader on Friday.
Mr Cleverly said: “I felt that we needed to deliver Brexit and then quickly move the conversation on to other important issues that face the country.
“I had hoped that the Conservative parliamentary party would support me to be the face and voice of that conversation.
“To do this I asked them to make a leap of faith, skip a generation and vote for a relatively new MP.
“It is clear that, despite much support, particularly from our party’s grassroots, MPs weren’t comfortable with such a move and it has become clear that it is highly unlikely that I would progress to be one of the final two candidates.”
In other developments:
– Boris Johnson’s former campaign manager Ben Wallace “hasn’t decided yet” whether to back him again in his latest party leadership bid
– Brexiteer Liam Fox announced he is backing Jeremy Hunt, who recently described a no-deal Brexit as “political suicide”
– Mr Johnson, Sajid Javid and Andrea Leadsom will take part in a private hustings for Tory MPs in the centre-right One Nation group
Security minister Mr Wallace ran Mr Johnson’s leadership campaign in 2016 and threatened to go “Game Of Thrones” on Mr Gove after he scuppered Mr Johnson’s chances, opening the door for Mrs May.
Asked on BBC Radio 4’s Today programme if he had decided whether to back Mr Johnson, Mr Wallace said: “I haven’t made a decision yet.
“The one thing I have learned from being inside a campaign is we’ve got another 10 days – your listeners will be dead bored.
“What we do need to do is make sure this race is about getting the right person to lead the country, but I’m not going to bang on about it.”
International Trade Secretary Dr Fox announced he is backing Mr Hunt because he wants to steer away from a no-deal Brexit.
Privilege to work with @LiamFox in Cabinet for many of the last nine years and very honoured by his support. He is an outstanding trade secretary. Looking forward to working with him to get a better Brexit deal and make the most of new trading opportunities across the globe. pic.twitter.com/GGSicmj1wY
— Jeremy Hunt (@Jeremy_Hunt) June 4, 2019
He said: “In this contest I’ll be backing my friend Jeremy Hunt, who is an impressive Foreign Secretary, who is an entrepreneur by background where deal-making is part of his DNA.
“I think he understands we have to send a message to Europe that we will leave if we cannot get an appropriate deal but we will try to get a deal.”