Launching his campaign at a circus tent on London’s South Bank, Mr Stewart accused his rivals of offering “fairy stories” on Brexit.
The Tory leadership contest officially began on Monday, with 10 candidates vying to replace Theresa May as party leader and prime minister.
On a busy second day of the official contest:
:: The candidates faced questions from Tory MPs, with one supporter of Michael Gove claiming his cocaine admission did not come up during his appearance.
:: Former chief whip Mark Harper claimed Mr Johnson still has to give “clear answers” on drug use.
:: Andrea Leadsom said she was against a second Scottish independence referendum, but would “never say never” to another vote.
:: A number of PM hopefuls clashed over whether the UK can leave the EU on 31 October, the current Brexit deadline.
Mr Stewart has sought to present himself as a straight-talking politician who tells it like it is, amid what he views as the disingenuous promises from the other candidates.
One of the key fault lines in the contest is over the prospect of a no-deal Brexit, with a number of candidates saying they would be prepared to walk away without an agreement in place with Brussels.
But Mr Stewart attacked those advocating such a scenario.
“It is not just no to a deal. It is no to everything. It is no to Europe, it is no to trade, it is no to parliament, it is no to reality. We are not a ‘no’ country,” he said.
“Underlying all these stories that the other candidates are putting forward that masquerade as optimism is a failure – a failure to grasp reality. What they are giving you is fairy stories.
“The way that you change that the world is being honest to the way the world is.”
Mr Johnson, the former foreign secretary and mayor of London, is the favourite to succeed Mrs May.
When asked if his slick leadership pitch would be forgotten about once Mr Johnson had launched his campaign on Wednesday, Mr Stewart said he trusted party members would “arrive at the correct answers” once his rival was subjected to proper scrutiny.
He said: “When you ask them, do you really – and I don’t want to make this too personal – do you really feel that this is the person that you want engaging with the detail and the future of your health and education system?
“Is this the person that you want writing the instructions to the nuclear submarines?
“Is this the person that you want embodying the nation on the world stage and guiding you through the most difficult choice that Britain has faced for 50 years?
“I trust the Conservative members to arrive at the correct answers.”
Compared to the likes of Mr Johnson, Michael Gove and Jeremy Hunt, Mr Stewart is seen as somewhat of an outsider in the leadership race.
And his chances may have been hampered further by his response to a question about opposition moves to try and take a no-deal Brexit off the table.
“I am entirely against no deal. I am entirely against peroration [suspending parliament],” Mr Stewart said.
“I haven’t read the details of this. My instinct is I would be wholly supportive of a move that tried to do that.”
But Mr Stewart later tweeted to confirm he would not be supporting the move, having read the details.
Shadow Brexit secretary Sir Keir Starmer has said Labour will use its opposition time on Wednesday to try and give MPs control of the parliamentary agenda on 25 June.
The motion – which has the support of the SNP, Lib Dems, Greens and Tory MP Sir Oliver Letwin – could be used to try and stop Mrs May’s successor pursuing no deal.
After a slew of candidates launched their campaigns on Monday, a number of others followed on Tuesday.
Ex-cabinet minister Mrs Leadsom branded herself an “optimistic yet realistic Brexiteer” as she set out her plans for a “managed” exit from the EU.
She described the new Brexit deadline of Halloween as a “hard red line” and claimed “politics has failed dismally” over the last three years, due to the failure to deliver on the 2016 EU referendum result.
Vowing to take the UK out of the EU this autumn should she win, Ms Leadsom said: “In all circumstances we are leaving the EU on 31 October this year.
“Our country and our party cannot afford any more indecisiveness.”
Promoting her Brexit proposals as a third way between leaving the EU without a divorce agreement, or not leaving at all, she added: “My managed exit offers sensible measures that sensible politicians both here in parliament and in the EU will, in my opinion, agree to.”
Launching his campaign after Mrs Leadsom, Mr Harper disregarded the October deadline.
He said he would be “comfortable” with a no-deal Brexit but his “preference” was to leave with a divorce agreement.
Mr Harper, who labelled himself a “serious underdog” in the race, added: “Where perhaps I will not make myself popular with my colleagues is when I say that it is not going to be possible to leave on 31 October.
“I would love to, I voted in parliament to leave on 29 March, I voted to leave on 12 April, I voted against extending Article 50 twice. But not enough people in parliament did so.
“I’m afraid it is not credible to say you can renegotiate the withdrawal agreement and get it through both Houses of Parliament by 31 October.”