He described himself as "less Homer's Iliad and more Homer Simpson" in the race to become the next prime minister, and warned that the Tory leadership race risked looking like a debate at the Oxford Union if the final candidates are all from similar backgrounds.
Candidates to become Britain's next prime minister clashed over Brexit strategy at their first debate on Sunday but the front runner, Boris Johnson, dodged the confrontation.
Meanwhile, the Environment Secretary Michael Gove, who came third in the first ballot with 37 votes, said the final two candidates should "believe in Brexit" and be able to deliver it and unite the Tory party.
The voting by MPs will continue until only two candidates remain.
But the race is on to decide who will challenge him.
Tory MPs will vote in the second bout of the contest to select Britain's next prime minister on Tuesday ahead of a live TV debate that will feature the front-runner and former foreign secretary, Mr Johnson.
And International Development Secretary Rory Stewart's campaign was boosted by the backing of Cabinet Office Minister and de facto deputy prime minister David Lidington.
But parliament has indicated it will try to stop a no-deal Brexit, which investors warn could roil markets and shock the world economy, while the European Union has said it will not renegotiate the Withdrawal Agreement that May agreed.
Tory leadership contest rules dictated that candidates needed to win at least 33 votes to have a chance of advancing today.
Tuesday 18th June 18.00: Results of second ballot.
The final two should be known by Thursday and then the members get to make the big choice.
If all of the candidates had hit that threshold, the one with the fewest votes would have been eliminated.
He repeatedly challenged the others to detail their own Brexit plans and accused them of "machismo".
"This is a two-horse race, and we know one of these horses - it's Boris ..."
Rory Stewart has been the big gainer in the lower rankings by leapfrogging into fourth place with an extra 18 supporters to nearly double his vote to 37 and breathing down Gove's neck.
He said: "In so far as my words have given offence over the last 20 or 30 years when I have been a journalist and people have taken those words out of my articles and escalated them, of course I am sorry for the offence they have caused".
Mr Johnson won the support of former leadership contender Andrea Leadsom, who said he would be a "very good leader for our country".
Mr Gove and Mr Javid also increased their level of support - by four and 10 votes to 46 and 33 votes respectively. He said that he did not want a disorderly no-deal Brexit but that the government had to be ready for that eventuality.
Foreign Secretary Jeremy Hunt took a swipe at John Bercow, accusing the Commons Speaker of siding with MPs plotting to thwart Brexit. "The idea that the British parliament can be pushed aside when such a crucial decision is to be made is fantasy".
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