In an interview with Sky News, Stewart was asked to respond to suggestions that Johnson, the former foreign secretary, would go ahead with such a drastic course of action to resolve Brexit.
Health Secretary Matt Hancock, former pensions secretary Esther McVey and ex-immigration minister Mark Harper are considered the three most vulnerable to dropping out.
Seven candidates are left in the next round of voting and the bookies believe Mr Johnson is the hot favourite to win the contest and become Prime Minister.
"Thank you to my friends and colleagues in the Conservative & Unionist Party for your support".
The elimination of Ms McVey and Mrs Leadsom means Mrs May will not be replaced by another female in Number 10.
Finance minister Philip Hammond, who has not publicly endorsed a candidate, wrote on Thursday to all remaining leadership contenders to urge them to stick to existing budget rules until at least the next scheduled election in 2022.
Conservative MPs hold their first secret ballot in the governing party's leadership contest as they begin whittling down the contenders.
Foreign Minister Jeremy Hunt was a distant second with 43 votes.
"We face a crucial choice: who can negotiate some better choices than the bad ones we face", he said. "This serious moment calls for a serious leader", he tweeted.
And a spokesperson for Michael Gove's campaign said: "Everyone had written us off. People said we were going backwards".
Harper gained 10 votes while Leadsom and McVey achieved nine votes. But we gained support and are in touching distance of second.
Cheryl Gillan said there were no spoiled ballots or rejected votes.
International Development Secretary Rory Stewart snuck through in seventh place with 19 votes after running an original social media campaign that endeared him to more liberal party members - and the British public at large.
Raab, like Johnson, has warned that he was ready to take Britain out of the European Union without an agreement when the new Brexit deadline arrives in October, if the European Union does not offer better terms.
Ms McVey said she would speak to the remaining candidates to decide who is "best placed to deliver" on her programme of a "clean break" from the European Union and investment in public services.
Defence Secretary Penny Mordaunt, who is supporting Mr Hunt's campaign, told the Press Association: "I think he's attractive to many sides of the party because he's a serious individual".
He said: "You build on that by saying, this message I am selling, about being fearless in the centre ground and getting out and listening to people, is extraordinarily popular".