Campaigners are calling for Boris Johnson to ‘face the public’ and take part in live TV debates as Sky was forced to cancel its planned event.
The front runner in the Tory leadership contest was branded a "bottler" by allies of Jeremy Hunt for ducking a TV showdown.
Sky News invited the leadership rivals to take part in the head-to-head debate on Tuesday night hosted by Kay Burley but said it would be cancelled due to Mr Johnson's decision not to attend.
The broadcaster has now invited both men to take part in a debate on July 1.
The head-to-head format meant it would not have been possible for Mr Johnson to be replaced by an empty podium on Sky as he was in a Channel 4 debate earlier in the leadership contest.
An ally of Mr Hunt said: "Bottler Boris and his complacent campaign have shown they can't trust their candidate to turn up and perform."
A Sky News spokesman said: "Jeremy Hunt has agreed to take part, but Boris Johnson has so far declined the invitation. We stand ready to host a debate tomorrow evening if both candidates make themselves available.
"Without both candidates, tomorrow's debate will not take place. But we will reissue our invitation for Mr Hunt and Mr Johnson to debate live on Sky News next Monday, July 1."
A spokesman for Mr Hunt's campaign said: "Whoever wants to be prime minister must face up now to the intense scrutiny that comes with the job, anything less is deeply disrespectful to our members.
"Trying to duck debates and run down the clock until after postal ballots have been returned is just cynical and complacent.
"Boris Johnson must stop trying to slink into No 10 through the back door and come clean about his programme for government."
The ERS has also called for the Conservative leadership candidate to take part in the debate.
Darren Hughes, ERS chief executive, said: “TV debates have become a core and established part of our elections in the UK – a chance to put candidates under the spotlight and scrutinise their policies. The fact that the electorate for this contest is restricted to Conservative Party members means the need for full and proper public scrutiny is even more vital.
“The public have a right to hear the views and policies of our potential next Prime Minister. By appearing to hide from scrutiny, Boris Johnson is denying us all a vital democratic opportunity.
“In only speaking to a handful of voters, Johnson is dismissing the very public he seeks to serve. Mr Johnson should do the right thing and agree to fully take part in open, transparent debates and set out his views before the country. To fail to do so would only increase distrust and let voters down at this crucial time in our politics.”