Mr Johnson’s opponents have teamed up to write an open letter stressing their commitment to taking part in all the upcoming televised debates.
So far, the former foreign secretary has only answered six questions from journalists during the whole campaign.
But that hasn’t stopped him opening up a huge lead in the first ballot of the contest.
Mr Johnson’s team said he is “in discussions” with broadcasters.
In September last year, Mr Johnson told Sky News that TV debates were an “essential” part of politics, adding: “The public does need to see interchange between their potential leaders.”
He also backed a Sky News’ campaign to establish an independent commission to ensure TV debates become a regular fixture of UK elections.
In a joint statement, fellow Tory contenders Jeremy Hunt, Michael Gove, Dominic Raab, Sajid Javid, Rory Stewart and Matt Hancock – who has since pulled out – said the leadership contest was “a critical moment” for both the UK and the Conservative Party.
They wrote in the open letter: “The next Conservative leader, and prime minister, will have the crucial task of uniting Britain behind a new vision – not only to deliver Brexit, but to define what comes next.
“This leadership contest provides an important opportunity to debate, to shape and to define the ideas which will underpin those competing visions.
“That is why we are committed to taking part in the Channel 4 televised debates this Sunday and the BBC programme next Tuesday.”
The TV debates follow a series of hustings events in parliament for the Conservative leadership candidates to make their case to Tory MPs.
The final two candidates will also take part in 16 hustings events in front of Conservative Party members in every region and nation of the UK, starting from 22 June in Birmingham.
Those campaigning against Mr Johnson warned his strategy of avoiding media scrutiny could land the Tories with the same sort of leadership coronation that delivered victory for Theresa May, without her being stress-tested under the spotlight.
Responding to a video of Mr Johnson’s comments from September, Mr Stewart tweeted on Friday: “So pleased to hear this – well done Boris – look forward to seeing you in the debate on Sunday!”
One of Mr Stewart’s supporters, Justice Secretary David Gauke, posted: “#IAgreeWithBoris”.
And Work and Pensions Secretary Amber Rudd, who is backing Mr Hunt, wrote: “Good sense from Boris here.”
A campaign spokesman for Mr Stewart said the next leader must demonstrate they have the capability to “win back old voters and win over new audiences”.
He added: “Any candidate who seeks that mantle can hardly opt out of a public debate.
“If any candidate ducks that duty, there is a simple question we should ask: ‘What have you got to hide?”‘
Mr Raab called for a “proper debate”, saying: “I’m looking forward to the first televised debates on Sunday and I hope that everyone gets involved – we should have a proper debate on the vision for the country.”
Sky News understands Mr Raab’s team organised the joint statement from Tory leadership candidates.
Meanwhile, Mr Hancock has pulled out of the race to support another candidate with a better chance of winning the 33 votes needed to get past the next round.
The Times reported the health secretary met Mr Javid, the home secretary, but the meeting appears not to have resulted in any agreement and he is now thought to be more likely to back Mr Gove or Mr Hunt.
Amber Rudd, the work and pensions secretary, told Mr Johnson it was his duty to debate with his rivals and “get out and do the TV debates”, according to the newspaper.