Horner, the Red Bull team boss, was at the center of accusations of inappropriate behavior towards female colleagues. Following an internal investigation, Red Bull's board dismissed the complaint last week.
The next day, anonymous emails containing messages purporting to involve Mr. Horner were leaked. Horner refused to say whether the messages were genuine, and Verstappen denied being the source of the leak.
Jos Verstappen, who drove in F1 from 1994 to 2003, told BBC Sport he made the comment after a fight with Horner in Bahrain.
He will not be attending this weekend's Saudi Arabian Grand Prix as he is participating in a rally.
Max said he spent the days between the two races with his father and said Jos and his manager Raymond Vermeulen would always be together as long as he is in F1.
“I don't think I would be in F1 without them around me,” Verstappen said.
Asked if he expected Horner and his father to put their differences aside, Max said, “Generally, with or without an argument, there's always something that can be worked out. Either way. Everyone is man enough and respectful enough.
“I don't always agree with everything that happens in F1. That's why sometimes it's good to discuss things and sometimes you agree to disagree. That's what happens in relationships. That’s the way things are.”
Verstappen rejected calls from FIA president Mohammed Ben Sulayem to offer public support to Horner in Bahrain.
“I'm not going to say yes or no,” Verstappen said. “He came to me personally.”
Verstappen has denied media claims that he could be tempted to leave Red Bull for Mercedes following the Horner controversy.
Asked if he would stay until the end of his contract in 2028, Verstappen said: “That was always the intention of the contract. That's why we signed for this long to be here. And of course it's for performance. he said. of cars, and beyond 2026.
“There's a bit of a question mark with the new regulations, but we knew that when we signed the contract.
“But I also know what they've done for me in my career. I'm definitely going to stay with this team because I really enjoy this team and I know what they've done for me within the team. Because I'm happy. As long as we're performing, there's no reason to leave.”
Mercedes driver George Russell said every team on the grid would be interested in signing Verstappen if he was available.
Russell said: “Every team wants the best possible driver line-up and Max is the best driver on the grid right now. So if any team has the chance to sign Max, we would 100% take it. “We're going to get that,” he said.
“The problem is more on the other side, on his side and on the Red Bull side. Obviously there's a lot going on there. We don't know what's really going on behind closed doors and at the end of the day it's That has nothing to do with us.”