Boris Johnson has refused to answer questions on 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 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.
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 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” but, rather than answer the question, spoke about “open platforms on the back of new Routemaster buses in London” when he was London mayor.
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”.
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 allegedly heard saying the MP had ruined a sofa with red wine: “You just don’t care for anything because you’re spoilt. You have no care for money or anything.”
Residents also reportedly heard shouting in the early hours of Friday morning.
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 correspondent Helena Wilkinson
Boris Johnson would have preferred his politics – not his private life – to be making headlines.
As we enter the final stage of this leadership campaign, the scrutiny of the two men who want the top job will no doubt increase.
There will be intense focus on their every move – their past, their present and their future.
It’s not surprising, given the importance of the job they want – running the country.
But does what allegedly happened in the London flat Mr Johnson shares with his partner really matter?
His critics will say yes.
They argue that we need someone of good character who can make difficult decisions and work under pressure.
Supporters of Boris Johnson disagree. Whatever happened, they say, was an entirely private matter between two people in a relationship which should never have been recorded by a neighbour.