Boris Johnson has refused to answer questions about reports of a row between him and his partner in which police were called.
Speaking at a Tory Party hustings in Birmingham, Mr Johnson said people did not "want to hear" about the reported row between him and Carrie Symonds.
The Guardian had said Ms Symonds was heard telling the Tory MP to "get off me" and "get out of my flat".
Police said they spoke to all occupants of the address, who were safe and well.
In the first of 16 hustings events, Mr Johnson and Jeremy Hunt made their pitches to an audience of party members to succeed Theresa May as prime minister.
Mr Johnson was asked about the incident a number of times by hustings moderator Iain Dale, an LBC radio presenter, but each time avoided answering the question.
After being accused by Mr Dale of ducking the question, Mr Johnson did not respond directly, instead saying: "People are entitled to ask me what I want to do for the country."
Mr Dale pressed again, telling Mr Johnson: "If the police are called to your home it makes it everyone's business.
"You are running for the office of not just Conservative Party leader, but prime minister, so a lot of people who admire your politics do call into question your character, and it is incumbent on you to answer that question."
In response, Mr Johnson accepted this was "a fair point" and said he "was a man who keeps to political promises".
Pressed another two times on the issue, Mr Johnson said it was "pretty obvious from the foregoing" he would not be making further comments on the incident.
Mr Dale was jeered by members of the audience at one point during the exchange, but Mr Johnson responded by telling the crowd "not to boo the great man".
The report of the row between Mr Johnson and Ms Symonds in the Guardian said a neighbour had told the newspaper they heard a woman screaming followed by "slamming and banging" in the early hours of Friday.
It said that in the recording - heard by the Guardian, but not by the BBC - Mr Johnson was refusing to leave the flat and telling the woman to "get off" his laptop before there was a loud crashing noise.
Ms Symonds is reported to be heard saying that the MP had ruined a sofa with red wine, adding: "You just don't care for anything because you're spoilt. You have no care for money or anything."
'Important public interest'
The neighbour who made the recording has since come forward to explain his reasons for contacting the Guardian about the row.
Tom Penn, 29, said he and his wife had concerns for their neighbour's safety.
He told the paper: "Once clear that no one was harmed, I contacted the Guardian, as I felt it was of important public interest.
"I believe it is reasonable for someone who is likely to become our next prime minister to be held accountable for all of their words, actions and behaviours.
"I, along with a lot of my neighbours all across London, voted to remain within the EU. That is the extent of my involvement in politics."
Mr Johnson's relationship with Ms Symonds - a former director of communications for the Conservative party - became public after Mr Johnson and his wife, Marina Wheeler, announced they were divorcing in 2018.
Ms Symonds was seen in the audience during Mr Johnson's leadership campaign launch on 12 June.
By BBC News political correspondent Jonathan Blake
Nobody can say that Conservative Party members don't have a choice.
The contrast between the two candidates to be their new leader and the UK's next prime minister was clear to see on stage in Birmingham.
Both men gave performances which reaffirmed their strengths and weaknesses as politicians.
Boris Johnson delivered soaring rhetoric, swerved the specifics and worked the room with cheeky asides and shameless flattery.
Jeremy Hunt stressed his serious side, played it straight and gave carefully considered answers.
Mr Johnson looked a little uncomfortable at times, asking at one point "how much longer have we got?"
Mr Hunt seemed keen to convey a softer side - his best friend coming out on the last day of school was one of many anecdotes.
Supporters of each will have likely left the event further convinced that their favourite is the man for the job - and those yet to decide have some food for thought.
One down, 15 to go.