Andrew Gwynne, the shadow secretary of state for communities and local government, said Johnson was "completely unsuitable" to be prime minister.
"Boris is appearing at something like 18 hustings around the country, has already appeared last week on the BBC debate and is very much undergoing scrutiny through the media every day", she told the Today programme.
The Foreign Minister and New Zealand First leader said Mr Johnson is not just a character, he's got character. Organizers were forced to cancel the event after Johnson refused to take part.
Talks are "not going to be easy" but "it's not impossible either", because a deal is in both sides' interests, Hunt said.
Hunt said he was not going to comment on Johnson's private life.
Mr Johnson, 55, is the favourite to win a vote of 160,000 Conservative Party members to decide who will be the next prime minister. Betting markets give him a 79 percent implied probability of winning the top job, down from 92 percent last week.
Johnson, 55, who served as London mayor for eight years, has cast himself as the only candidate who can deliver Brexit on October 31 while fighting off the electoral threats of Nigel Farage's Brexit Party and Jeremy Corbyn's Labour.
London Metropolitan Police said it responded to a call from a local resident, but that "all occupants of the address. were all safe and well".
Symonds, a former Conservative Party press officer, has remained firmly out of the public eye since the reported quarrel Friday when a neighbor hear shouting, screaming and banging at the home the couple shares.
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But his intervention over Johnson's refusal to engage with the media will be seen as a coded reference to his opponent's appearance at the first hustings of the leadership race on Saturday, in which he stonewalled persistent questions about the incident, which took place in the early hours of Friday morning.
Johnson declined to comment on the argument in an interview with BBC News.
Hunt was quick to point out during the interview that if the Brexit moves were not carried out properly then Britain could "trip into a general election, Jeremy Corbyn will become prime minister and then we'll have no Brexit at all".
"I don't think (audience members) want to hear about that kind of thing, unless I'm wrong", Mr Johnson said when asked about the incident.
The victor of the contest will replace May, who stepped down as party leader after failing to secure Parliament's approval for her Brexit deal. "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 behaviors".
"Stuff happens at home all the time. someone spills the wine, we can't really be making headlines out of that", supporter Hasnain Ahmed, 23, told AFP news agency.
Mr Brown said: "Jeremy Hunt is every bit as callous as his Tory colleagues - consistently voting in Parliament against the right for European Union nationals to remain in their homes, while slashing welfare spending and giving tax cuts to the rich". It's entirely possible and reasonable to have your own view but to then be realistic and say, 'I'm very unlikely to get my view through because Parliament is unlikely to deliver it'.