Fifa president Gianni Infantino says he hopes the "facts will emerge" around "anonymous complaints" made about him that led to a criminal investigation.

Last week, prosecutors in Switzerland opened proceedings against Infantino over an alleged secret meeting with Swiss attorney general Michael Lauber.

Both men deny any wrongdoing.

In a letter to the football governing body's member associations, Infantino said any meetings were "in no way secret and most certainly not illegal".

However, the 50-year-old Swiss admitted the investigation had already "caused considerable damage to Fifa as an organisation and to myself as its president".

Infantino is not stepping down from his role while the matter is dealt with.

In his letter, which has been seen by BBC Sport, Infantino writes: "Some anonymous complaints were filed against me in the canton of Bern.

"Not knowing the content of those anonymous complaints, we can only speculate as to why they were filed and who is behind them. Hopefully the facts will emerge one day."

Infantino says the meetings with Lauber were broadly to discuss the fact that the attorney general's office was investigating a series of criminal allegations in which Fifa was a damaged party.

"I obviously also remain at your disposal for any clarification or further information that you might need, as this is also about our organisation, your organisation, the one that we all represent and must defend," said Infantino, who added that he had received messages of support since the investigation was announced.

"The mere fact of meeting a state prosecutor ought to be the best guarantee that any such meeting is legitimate.

"If there were even the slightest suggestion of any wrongdoing, a prosecutor would and should intervene immediately to prevent it, as part of his or her basic legal and professional responsibility."

Neither Lauber nor Infantino have been able to recollect the specific details of their final meeting in 2017.

Earlier this week, Fifa deputy secretary general Alasdair Bell said: "It seems to me extraordinary that because someone doesn't remember the details of the meeting it's part of some criminal conspiracy involving the attorney general of Switzerland."