The Tory leadership outsider refused to echo senior Tories Philip Hammond and Ken Clarke who could potentially back a vote-of-no-confidence, saying: “I'm not going to take down a Conservative government.”
Questioned by The Independent at hustings in Westminster, Mr Stewart said: “We can stop a no-deal Brexit much more easily than that.
“I, and nearly 100 of my colleagues, would vote to prevent a no-deal Brexit without having to bring down a Conservative government.”
Mr Stewart also ruled out backing a Final Say referendum on Brexit, telling journalists it would be “catastrophic and divisive”.
A Remain voter in 2016, he refused to say how he would vote if the referendum was staged, saying he would be “trying to make a very difficult decision, extremely angry”.
Meanwhile, Sajid Javid, a leadership rival – and another former Remainer – said he would vote Leave if offered a second chance, adding. “We cannot as a country keep having this debate over and over again.”
And, playing the outsider card, the home secretary said: “I didn't go to the debating societies at Oxford or other places. I may not be the most confident speaker.”
Mr Stewart admitted his plan to re-boot Theresa May’s stalled withdrawal agreement could only succeed if he could win over Labour MPs, once in No 10.
Unlike the other candidates, the international development secretary has vowed to bring back the deal, arguing he could persuade “maybe a dozen” refusenik Tories to vote for it.
He said he would then reach out to Labour MPs, such as Lisa Nandy, who have said they want to deliver Brexit – but refused to vote with the outgoing prime minister.
Mr Stewart was cautious about whether he would achieve the necessary 33 signatures to clear the second round of the contest tomorrow, but said he would do so if people “do what they say”.
He was also asked if, as strongly rumoured he was an MI6 spy when working as a diplomat, but replied: “No.”