It came as a new poll revealed Mr Johnson as the clear favourite among Conservative Party members, with Mr Stewart trailing in last place.
The International Development Secretary has repeated criticised Mr Johnson throughout the race to be the next Prime Minister, accusing him of making false promises about Brexit and ruling out accepting a job in a Johnson cabinet.
Mr Stewart said: “Somehow he’s convinced Matt Hancock that he agrees with every word that Matt says, that he’s in favour of the softest of soft Brexits, he’s convinced Robert Buckland that he would never go for a no-deal and at the same time he’s got Mark Francois roaring ‘this man looked me in the eyes and promised we’re going out on the hardest of no-deal Brexits’.”
He made the comments during a grilling of the men hoping to be the UK’s next Prime Minister by journalists - from which Boris Johnson was once again conspicuously absent.
Mr Johnson was widely criticised for failing to appear at a debate between candidates on Sunday night and for avoiding media appearances throughout the campaign.
New YouGov research released this morning found 77% of Tory party members - who have the final say on who will become PM - think Mr Johnson would make a good leader.
Just 31% said they thought Mr Stewart would be a good leader.
Hard Brexiteer Dominic Raab was the second most popular candidate.
Mr Stewart, who is the clear outsider in the race to lead the Conservative Party, insisted today he has the necessary support to make it through the next stage of the competition so long as his supporters ‘do what they say’.
Tory MPs are holding a second round of voting tomorrow to choose a leader and any candidate with fewer than 33 votes will be knocked out.
Mr Stewart received 19 voted in the first round.
If all the candidates receive at least 33 votes, the person with the fewest votes will be knocked out.
The other remaining candidates - Sajid Javid, Dominic Raab, Michael Gove and Jeremy Hunt - were also quizzed by the media today.
Said he could ‘put Boris through his paces’ if he made it to the final two
Positioned himself as a change candidate, saying voters do not want to see battle between two Oxford educated old Etonians
Criticised Donald Trump for his attacks on Sadiq Khan
Attacked Rory Stewart for ‘trying to appeal to Labour voters’
Said he could renegotiate Theresa May’s Brexit deal
Spoke against speaker of the House of Commons John Bercow for ‘using his office to further a particular agenda’
Acknowledged risks of no-deal Brexit to business and manufacturing
Accused EU officials of briefing against him because they are afraid of him
Committed to having early budget to utilise Treasury’s ‘fiscal horsepower’
Said Brussels has ‘politicised’ Northern Ireland backstop
Pitched himself as candidate best qualified to solve Irish backtop
Pledged to ‘supercharge’ work on alternative arrangements
Said Donald Trump made a ‘mistake’ retweeting Katie Hopkins
Attacked Jeremy Corbyn for ‘sticking up for Iran better than for British working class’