After another vote by MPs, the candidates will go down to two.
Dame Priti Patel has been knocked out of the Tory leadership race in the first round.
Patel and five other candidates were running to replace Rishi Sunak. But she fell at the first hurdle with just 14 votes.
Robert Jenrick topped the poll with 28 votes, followed by the widely reported favourite Kemi Badenoch on 22.
James Cleverly received 21 votes, Tom Tugendhat won over 17 and Mel Stride gained 16.
A total of 118 votes were cast, meaning three Conservative Party MPs did not have their say.
Although Priti Patel’s leadership bid was shortlived, there is still a long way to go before the new Tory leader is crowned.
A further round of voting will take place on September 9, 2024, to get the ballot down to four, and they will then face an onstage hustings during the Conservative Party conference at the end of the month.
After another vote by MPs, the candidates will go down to two.
The wider party membership will then choose their leader, with the result expected to be announced on November 2.
After the result was confirmed, Ms Badenoch thanked her supporters, adding:
“It’s time to deal with hard truths today, rather than big problems tomorrow.
“I look forward to making the case for renewal around the country, with colleagues and members.”
In his statement, Mr Tugendhat paid tribute to his “friend Priti” and the “good Conservatives” he is competing against.
However, he added: “Only I can deliver the Conservative revolution that our party and our nation need.
“I will lead in opposition as I would as Prime Minister, by serving the British people, leading with conviction, and acting to make our nation better.
“That is my promise, and I always deliver on my promises.”
Patel has been a Conservative MP since 2010 and her elimination came as a surprise given that she is the most experienced of the candidates.
She became a key torchbearer for the party when she served as Home Secretary under Boris Johnson.
But she had positioned herself as a unity candidate in this race, arguing the party should not let “a soap opera of finger-pointing and self-indulgence” distract from the goal of winning the next election.
Speaking about the leadership contest, a Labour Party spokesperson said:
“The Tories have successfully slimmed down the pool of contenders from six people who each played their hand in 14 years of chaos and decline, to five people who each played their hand in 14 years of chaos and decline.
“From what we have seen so far, not one of them is prepared to learn from the lessons of the past.”