FIFA president Gianni Infantino has told national association bosses he hopes "the facts emerge" around who made the anonymous complaints which have led to the opening of a criminal investigation against him.

Infantino has written to the world governing body's member associations after the Swiss special federal public prosecutor opened criminal proceedings last week over meetings Infantino held with the country's attorney general in 2016 and 2017.

In the letter, which has been seen by the PA news agency, Infantino wrote: "This new investigation has now been opened by the Swiss special prosecutor because 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 attorney general Michael Lauber were broadly to discuss the fact that Lauber's office was investigating a series of criminal allegations in which FIFA was a damaged party.

He said in the letter to the associations that the meetings were "in no way secret and most certainly not illegal" but admitted that the mere existence of an investigation had already "caused considerable damage to FIFA as an organisation and to myself as its president".

Neither Lauber nor Infantino have been able to recollect the specific details of their final meeting in 2017, but FIFA deputy secretary general Alasdair Bell said on Monday: "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."

Infantino said he would fully co-operate with the investigation.And to the associations he said: "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.

"It goes without saying that the mere fact of meeting a state prosecutor ought to be the best guarantee that any such meeting is legitimate.

"Especially when you are meeting the most senior prosecutor in the country! Because 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."

Infantino said he had received many messages of support since it was announced that an investigation had opened.