"I don't want to give anybody the opportunity to think that there's anything going on that shouldn't be going on," Foster said, reiterating his personal 'rule' that he will not allow himself to be alone with a woman who is not his wife.
"When you have a married man with another woman and they're alone, some people may perceive that as there may be something taking place."
In response, host Martha MacCallum asked why a public figure being alone with a reporter would "evoke suspicion."
Doubling down on his position, Foster said people's thoughts about the situation will not affect his decision to conduct himself in a way he feels is appropriate.
"Their feelings and their concerns about being discriminated against do not trump my vow I made to my wife, and my belief I should not be alone with another woman who I'm not married to," the Southaven-area lawmaker said.
He added the reporter accusing him of sexism, Larrison Campbell, asked to accompany him and not the other way around.
Campbell should, therefore, be the one to make any concessions when it comes to having another person in his truck while they spend several hours together on the campaign trail, Foster claimed.
Earlier this week, Campbell wrote in Mississippi Today that Foster's campaign director Colton Robison offered her an opportunity to follow the candidate but said she would need a male colleague accompanying her.
“Perception is everything," Campbell quoted Robison as saying.
"We are so close to the primary. If (trackers) were to get a picture and they put a mailer out, we wouldn’t have time to dispute it. And that’s why we have to be careful."
According to Campbell, the decision ultimately stemmed from her gender. “The only reason you think that people will think I’m having a (improper) relationship with your candidate is because I am a woman,” she said she told him.
Fox News' Sam Dorman contributed to this report.