Verstappen Sr had been scheduled to drive in a Red Bull car at the annual Legends Parade in Spielberg, but pulled out of the event after accusing Horner of trying to block his participation.
Speaking to Dutch media outlet De Telegraaf, the former F1 driver said: "In the past few days I've heard from several sides that Christian Horner did everything he could to not let me drive, and otherwise to make sure that nothing would be filmed."
Horner was quick to dismiss those claims, but their feud escalated once again after Verstappen revealed he was 'done' with the Red Bull team principal.
'Scenario could have been avoided'
The recent war of words between the pair is the latest development in a season of ongoing exchanges, with Verstappen Sr previously criticising Horner for creating tension in the team.
Now, Red Bull's reigning champion has admitted the scenario is far from ideal for all parties involved.
Speaking to Sky Sports, the 26-year-old said: "Naturally, of course it's not nice. Not for myself, not for my dad, not Christian, not for the team.
"Of course you don't want these things to happen. My dad has been quite clear about the reason behind it and of course I can understand his opinion on it.
"Because at the end of the day, he gets asked to drive the car, finds out he's not wanted to drive the car.
"My dad doesn't actually care about driving the car, but he got asked: 'Please, do it for the Dutch fans?'.
"Red Bull, we have a great relationship with - home track - so I understand.
"On the other hand, I'm here to focus on the performance side of things, so I want a good relationship with everyone, but of course, this scenario could have been avoided."