At a press conference on the first day of pre-season testing in Bahrain on Wednesday, Wolff was the only one of five team representatives ready to answer questions about Horner's allegations.
He added: “F1 and the teams stand for inclusivity, equality, fairness and diversity. And F1 doesn't just talk about it, it lives it every day.”
“These are the standards we set for ourselves. We are a global sport, one of the most important sports in the world, and we set an example.”
“But there's been a lot of speculation going on in recent weeks, a lot of speculation that we've heard and a lot of things that are going on right now.
“This is not just a team issue. It's a whole F1 issue.”
Wolff was the first official to comment on the allegations against Horner, who remains Red Bull's team principal while the investigation is ongoing.
Red Bull has been unable to explain why the investigation has taken so long since the allegations first surfaced earlier this month.
F1, the sport's commercial rights holder, called on Red Bull to clarify the matter “at the earliest opportunity, following a fair and thorough process”.
Governing body the FIA said it would not comment until the investigation is complete, but added: “The FIA remains committed to upholding the highest standards of integrity, fairness and inclusiveness within the sport.”
Red Bull's lawyers will compile a report and submit it to the company's board of directors.
The identity of the lawyer has not been made public, and no other details about the scope of the investigation have been released.