The Tory leadership favourite blocked multiple questions about whether he knew how the snap, of the pair holding hands in the Sussex countryside, ended up in newspapers.
The photo emerged on Monday, in what was widely seen as an attempt to squash suggestions that they had split – following their noisy altercation last week, which led to the police being called.
Quizzed, on LBC radio, if he knew the photo was being released, Mr Johnson replied: “There are all sorts of pictures of me on the internet that pop up from time to time
“It is entirely up to newspapers to decide what they want to print.”
Mr Johnson, who has refused to answer any questions about the screaming row, which was recorded by a neighbour, also attacked such inquiries as a “waste of time”.
Defending his stance, he said: “The difficulty is that, the minute you say one thing, you obviously are bringing people, your loved ones, your family, into the public domain in a way that is not fair.
Asked again where the photograph had come from, Mr Johnson replied: “The longer we spend on things extraneous to what I want to do.....the bigger the waste of time.”
Mr Johnson was also asked whether he agreed with his supporter, Jacob Rees-Mogg, that his neighbours were “curtain-twitching Corbynistas”, but said: “I don’t want to get into casual name-calling.”
And, asked if he would himself call the police if he was concerned about an altercation in a neighbour’s property, he said: “I can’t imagine the circumstances in which I would do so.”
Mr Johnson also played down suggestions of a snap general election if he wins the leadership and MPs block his vow to deliver Brexit “deal or no deal” by 31 October.
“I think that the people of this country feel that they have been asked out to the polls quite a few times recently,” he replied – without denying an election might be necessary.
Denying he was trying to “dodge debate” by refusing to attend tonight’s Sky News debate – now cancelled – pointing to the many other events in the Tory leadership race.
“There are 16 hustings,” he said,” adding: “I have already done several with Jeremy [Hunt] and I look forward to doing many, many more.”
On Brexit, the frontrunner for No 10 warned the Tories would “continue to haemorrhage voters” if the UK did not leave the EU.
He claimed that “politics has totally changed” since March 29 and “we are staring down the barrel of defeat”.
He told LBC: “People are looking at this thing and thinking 'Parliament is just not going to do this'. But, actually, I think they are.”
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