Sky News has said it will be forced to cancel a debate between the two men vying to be the next Tory leader unless Boris Johnson agrees to take part.
The broadcaster hoped to be the first to stage a head-to-head debate between Mr Johnson and his rival Jeremy Hunt.
But it said Mr Johnson had “so far declined” its invitation and the event would not go ahead without him.
Mr Johnson has faced three days of questions over his private life after a row with his partner Carrie Symonds.
The former foreign secretary has declined to comment on the nature of the argument in Ms Symonds’ London home, which led to the police being called early on Friday morning.
He has also been accused of avoiding media scrutiny more generally, particularly on his Brexit policy.
Allies of Mr Johnson have stepped up their attacks on Ms Symonds’ neighbours, Tom Penn and Eve Leigh, for recording part of the argument and sharing it with the Guardian newspaper, suggesting their actions were “politically motivated”.
Jacob Rees-Mogg, the leader of the European Research Group of Brexiteers, described the couple as “Corbynista curtain twitchers”.
The couple have insisted they were motivated solely by concerns for the welfare of Ms Symonds after reportedly hearing raised voices and plates and glasses being smashed.
Mr Johnson remains the frontrunner in the contest to succeed Theresa May, with 160,000 or so Conservative Party members choosing their next leader by the end of July.
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Mr Hunt has challenged him to a series of live TV debates over the next 10 days.
But Sky’s planned debate on Tuesday now looks unlikely to go ahead.
“Jeremy Hunt has agreed to take part, but Boris Johnson has so far declined the invitation,” the broadcaster said in a statement.
“We stand ready to host a debate tomorrow evening if both candidates make themselves available,” it said. “Without both candidates, tomorrow’s debate will not take place.”
Mr Johnson has agreed to take part in a one-on-one debate with Mr Hunt on ITV on 9 July, which will take place after Tory members have started receiving ballot papers.
The two men are also taking part in a series of TV hustings for Tory members across the UK.
Mr Johnson and Mr Hunt took part in a five-way debate earlier in the leadership contest on the BBC last week, but Mr Johnson refused to join a similar event on Channel 4.
Responding to the Sky announcement, 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.”
Tory leadership race: Sky set to cancel Johnson-Hunt debate}