Following complaints from a female employee, Horner is under investigation by Red Bull's Austrian energy drinks parent company for his behaviour.
As part of the probe, Horner was recently interviewed by an independent barrister who has been appointed to draw together evidence of the unspecified allegations at the heart of the matter.
Horner has remained in position while the investigation is underway and attended the recent shakedown of Red Bull's new RB20 car at Silverstone as well as the official launch at its Milton Keynes factory.
But with the new F1 season looming, and there being a risk of the matter casting a cloud over the opening race in Bahrain, grand prix racing's chiefs last weekend urged Red Bull to make it a priority to conclude its investigation as quickly as possible.
"We have noted that Red Bull has instigated an independent investigation into internal allegations at Red Bull Racing," said a statement from F1.
"We hope that the matter will be clarified at the earliest opportunity, after a fair and thorough process and we will not comment further at this time."
With team personnel now travelling to Bahrain, there remains no official word from Red Bull on the progress of the investigation, nor any hint of potential action.
And while that may not be ideal for F1 in getting the matter resolved before cars hit the track, Marko thinks it is right that Red Bull takes its time to evaluate all the evidence in detail – rather than rush a decision for the sake of it.
Speaking to Red Bull's ServusTV channel about the Horner situation, Marko said: "As you know, this is an internal investigation.
"The sooner a result is available, the better because of course, rumours and other stories are bound to sprout due to the long duration.
"[But] I think Red Bull has reacted very well in this matter. The long duration of this investigation is not their fault. They are endeavouring to [have] a fair investigation and then react accordingly."
Horner said at the RB20 launch that support within the team had not wavered while the investigation was underway, even if the events had been a distraction.
"I think that the team is gearing up for the season ahead and we're in very good shape," he said.
"We're fully focused on going racing. Looking forward to being in Bahrain next week and seeing RB20 run. And the one thing that focuses everybody's attention is the car. We're very united and together in that focus."
Additional reporting by Ruben Zimmermann
