Mr Johnson said it was "simply unfair" to "drag" his loved ones into the political arena over the late-night quarrel in the early hours of Friday that has threatened to derail his campaign.
But on LBC Radio, he was repeatedly challenged over whether his campaign was behind the release of a picture of him with Ms Symonds in an attempt to show their relationship had not broken down.
In testy exchanges, he said there are "all sorts of pictures of me out on the internet which pop up from time to time".
When host Nick Ferrari suggested his hairstyle indicated it was an old picture, he said: "This conversation is now descending into farce."
Mr Johnson had kept out of the public eye since the news broke on Friday about the row at the south London home he shares with Ms Symonds.
Police called by worried neighbours after his partner was heard screaming and shouting "get off me".
Mr Johnson's campaign attempted to step up a gear with a series of media appearances and events following claims he was a "coward" from leadership rival Jeremy Hunt for shying away from debates.
In his first interview since the incident, Mr Johnson told the BBC on Monday night: "I do not talk about stuff involving my family, my loved ones.
"And there's a very good reason for that. That is that, if you do, you drag them into things that ... in a way that is not fair on them."
On Brexit, Mr Johnson said "politics has totally changed" since March 29 and "we are staring down the barrel of defeat" which would focus minds in Parliament.
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."
He said that "it is vital as a country that we get ready to come out without an agreement if we must" but argued that it would be "bizarre" for the European Union to impose tariffs on trade in that event if the two sides were looking at a future deal.
In his BBC interview, Mr Johnson called for "creative ambiguity" over the £39 billion cost of the UK's Brexit divorce deal, suggesting this could break the deadlock.
The former Vote Leave leader, who hopes to become prime minister, also called for a "commonsensical" no-deal Brexit to be left on the table to allow the "incubus" to be "pitchforked off the back of British politics".
"This is an incredibly difficult situation and Boris needs to explain how he will deal with both sides of the Conservative Party that have concerns and try and break the impasse with the European Union," she told BBC Radio 4's Today.
"Enthusiasm and optimism is not sufficient."