The underdog admitted he had been a Labour party member as a teenager – as he also acknowledged he was unable to reveal whether he had ever been a government spy.
Speaking ahead of the next round of voting of Tory MPs, Mr Stewart also ripped into Boris Johnson for telling both wings of the party what it wants to hear with contradictory versions of his Brexit plan.
Describing the tactic as “alarming” he said: “The only way we are going to have stability in our government, or our party, or our country, is if people trust us.”
Mr Stewart made clear he opposed Mr Corbyn’s economic and foreign policy but, asked if there were similarities between them, replied: “There’s something in that.”
Speaking to BBC Radio 4, he added: “One of the things he has done is he has completely transformed the party membership – quadrupling the number of members.
“He simply did it because he enjoyed talking to people and he believes in what he said.”
“One of the things that I found so invigorating about it was that it feels much more like old-fashioned politics.”
The international development secretary has succeeded in rattling the other rivals to Mr Johnson – with Sajid Javid, the home secretary, admitting he is “taking some support” from all over them.
He received the surprise backing of David Lidington, Theresa May’s ‘deputy’, but needs 14 more votes than the 19 he received last Thursday – and to avoid finishing last –for his leadership bid to remain alive.
As his campaign takes off, Mr Stewart is facing increasing scrutiny about his past in the UK diplomatic service, with postings in Jakarta, Indonesia, and as the British representative to Montenegro in the wake of the Kosovo crisis.
He was the coalition deputy-governor of two provinces in southern Iraq following the 2003 invasion.
The Daily Telegraph reported that Mr Stewart was hired by the Secret Intelligence Service as a “fast track” entry after he left Oxford University in the 1990s and left after seven years.
At a hustings on Monday, Mr Stewart denied he had worked for MI6 – but he admitted he would not be able to give an honest answer if he had done so.
The BBC’s Nick Robinson asked: “You can't really answer the question whether you were a spy or not, you can just simply say you served your country?”
Mr Stewart replied: “I definitely would say I served my country and, if somebody asked me whether I am a spy, I would say no.”
He later retweeted a comment from Tom Tugendhat, the foreign affairs committee chairman, who said on the Telegraph allegations: “If he did, he risked everything in the shadows defending our nation.
“If he didn't, he risked everything in Iraq trying to build the peace. Whoever these Whitehall sources are need to seriously rethink their ethics.”