The wider Red Bull GmbH company has launched a probe into Horner and he has faced lengthy questioning by an independent barrister who was appointed to draw evidence of the unspecified allegations.
Horner acknowledged at the launch of the RB20 that the matter had been a "distraction" when lightly addressing the story, for which the media had been told not to probe too far.
On the second day of pre-season testing in Bahrain, the Red Bull F1 team principal then faced his first official F1 press conference, which was streamed live to remote media while on-site journalists were not briefed on what questions would be permitted beforehand.
After initially addressing the RB20's early form, with Max Verstappen topping the first day of testing by 1.140 seconds, a question was put to Horner regarding the relationship between the main Red Bull team and its sister RB squad.
This comes amid concerns from rivals, led most notably by McLaren team boss Zak Brown, about one overarching party being able to own two teams competing in the same league and the possible advantages this may offer in terms of efficient operating under a cost cap. Horner spoke for three minutes and 37 seconds on the issue.
He was then asked directly about the investigation: "For Christian, you said it was business as usual at Red Bull. But it's not business as usual when the CEO is accused of inappropriate behaviour. So how can people take this investigation seriously when you've not been asked to step aside while it's in process?"
Horner replied: "As you're well aware, there's a process going on which I form part of. And as I form part of that process, I'm afraid I cannot comment on it."
Horner was then given a follow-up question about whether the matter was still a distraction, as he had conceded at the Red Bull team launch on 15 February, and about F1's own statement calling for the matter to be "clarified at the earliest opportunity, after a fair and thorough process".
Horner again declined to comment on anything relating to the investigation, although he did touch upon wanting a swift conclusion, as per F1 and the FIA's desires, while Red Bull partner Ford has also stated it was monitoring the situation.
He said: "Look, I'm dreadfully sorry, but I really can't comment on the process or the timescale.
"I think obviously everybody would like a conclusion as soon as possible, but I'm really not at liberty to comment about the process."
Horner avoided giving a direct answer to matters that he had previously discussed and the 20-minute press conference ended with the Red Bull boss being asked whether he felt his team was ahead after the first day of testing, and to recall his reaction when the technical team had presented its ideas during 2023 for the RB20 to mark a major change over its dominant predecessor.
