While Murray, who split with Stanton in December, first played coy about the PDA pics obtained exclusively by ET, he eventually fessed up to enjoying a "great dinner" with the mother of two.
"You know, we're trying to deal with stuff in a more private manner now, obviously, and we just kind of want people to respect that, and especially because it's a tough situation with the kids, and we don't want to kind of fully dive into anything, because we're thinking about them as well," he shared.
The Atlanta native also offered some context as to why the pair were reuniting after months apart.
"This is the first time I've seen her in a while. When I came out this week, I came for one of my friend's events, and I did some other stuff while I was here, and we ran into each other and stuff," he continued. "You know, we just had long conversations. They were conversations that needed to be had, and [we had] a great dinner and everything like that."
Murray and Stanton were one of three couples who got engaged during the season finale of Bachelor in Paradise this summer, and though their relationship lasted several months off-camera, Murray said they felt the pressure of "outside forces" upon returning home.
"It was a good evening. We had a good time. Whenever we're together, especially outside of the show and outside all the drama, it's always been a good relationship," he revealed. "There were just so many outside forces and outside factors that got involved after we were together on the show, and it was unfortunate for a little bit."
"We went through a lot," he added. "We went through a lot more than people understand."
As for the current state of the pair's relationship, Murray said it's "tough."
"There's a possibility for anything," he confessed of a possible reconciliation, though he described himself as "single" for the moment.
"I am single right now, so I'm traveling a little bit," he continued. "I'm having some fun and doing some things and enjoying some people, meeting people."
"It's tough going into detail about it. Like I said, I don't like talking about my relationships unless everything is great and there's positive things to be said, and there are positive things to be said of course, but there's a lot of things that we still need to talk about, just for moving on as friends or anything in the future, and we're beginning to do that," he added.
"This week was good, seeing each other, so we could engage in good conversation, and we could talk about the things in the past and be mature individuals and adults," Murray said. "And that's what you do, you talk about things. Everything, as of right now, is fine."
As for the future, Murray said that he seems himself married and having kids, admitting "that's the one thing i'm missing in my life."
"I'm also not going to settle," he added. "You want to be with somebody the rest of your life, not get divorced."
ET caught up with Stanton last month, where she opened up about her split with Murray for the first time, calling the break up "a little hard."