“One of the things that has been said about how you conduct your personal life is you will not eat alone or meet alone with a woman,” Mr Vittert said, referring to remarks in an infamous 2002 profile of Ms Pence in The Hill, that resurfaced in 2017 when he was vice president.
“How would that work out if you had a female vice president?”
Mr Pence replied with an ironic smile: “That’s a very clever question. It really is.”
The evangelical Christian told the audience that it was a “promise that my wife and I made to one another” that wasn’t controversial until after he was elected to the vice presidency.
“When I was first elected to Congress, I did an interview about the fact that we kept our family close in public service. Somebody asked us about some of the promises we’ve made to one another, and I remember I said, ‘Well I promised her that I wouldn’t dine alone with a woman that’s not my wife’,” he said.
“Somebody unearthed that quote and it became quite an issue.”
The unearthed quote, along with a disputed claim that he referred to Ms Pence as “mother”, led to unfair criticisms from liberals and sections of the media, Mr Pence added.
He said he didn’t want to impose his values on how other people chose to “manage” their marriage, but pointed to a 2017 New York Times poll that found a majority of couples agreed with his stance.
“In the wake of those tragic circumstances around the MeToo movement, it seemed to go away,” Mr Pence added.
Mr Vittert then cracked a joke about how he didn’t have the conservative Republican quoting New York Times polls “on his bingo card”, before moving on to other topics.
Mr Pence earlier praised Iowa Governor Kim Reynolds, when her name was mentioned as a potential VP.
The former Indiana governor is languishing in fifth place with 5.1 per cent in Republican primary polling, according to FiveThirtyEight.com.