Mosley has been FIA president for 15 years
Max Mosley has pledged to carry on as president of the FIA, motorsport's governing body, despite allegations about his private life.
In a statement, Mosley apologised for any embarrassment caused to the organisation and its members.
But the 67-year-old added that he will open legal proceedings against those who had conducted a "covert investigation" to discredit him.
"I will not allow any of this to impede my commitment to the FIA," he said.
The News of the World carried a report on Sunday claiming Mosley had taken part in a "Nazi-style orgy in a torture dungeon".
The Briton had been advised not to travel to this weekend's Bahrain Grand Prix, with Formula One boss Bernie Ecclestone saying the Bahraini royal family "would not like" his attendance in the Kingdom.
In response, Mosley sent the letter to the various presidents of the national FIA clubs, all members of the FIA senate, the World Motor Sport Council and the World Council for Mobility and the Automobile.
He wrote: "From information provided to me by an impeccable high-level source close to the UK police and security services, I understand that over the last two weeks or so, a covert investigation of my private life and background has been undertaken by a group specialising in such things, for reasons and clients as yet unknown. I have had similar but less well-sourced information from France.
"Regrettably you are now familiar with the results of this covert investigation and I am very sorry if this has embarrassed you or the club.
I need to repair the damage to my immediate family who are the innocent and unsuspecting victims of this deliberate and calculated personal attack
"Not content with publicising highly personal and private activities, which are, to say the least, embarrassing, a British tabloid newspaper published the story with the claim that there was some sort of Nazi connotation to the matter. This is entirely false.
"It is against the law in most countries to publish details of a person's private life without good reason. The publications by the News of the World are a wholly unwarranted invasion of my privacy and I intend to issue legal proceedings against the newspaper in the UK and other jurisdictions.
"I have received a very large number of messages of sympathy and support from those within the FIA and the motor sport and motoring communities generally, suggesting that my private life is not relevant to my work and that I should continue in my role. I am grateful and, with your support, intend to follow this advice.
"I shall now devote some time to those responsible for putting this into the public domain but, above all, I need to repair the damage to my immediate family who are the innocent and unsuspecting victims of this deliberate and calculated personal attack."
Mosley, the son of former British Union of Fascists leader Oswald Mosley, has been FIA president since 1993.
Mosley, who is not an employee of the FIA and whose role is unpaid, has been a prominent figure in European politics, pushing through a series of road-safety measures.
A representative of the road-car manufacturers involved in F1 said they had no comment at this stage.
F1 teams have no direct influence on Mosley's position - he is elected by the FIA membership of national automobile clubs and motorsport bodies and his latest four-year term does not expire until October 2009.
The body that can bring direct pressure on to Mosley is the FIA senate, which is made up of senior representatives of the national automobile and sporting clubs.
Below that are two FIA world councils, one representing the automotive industry, and one from the sporting side.
A spokeswoman for the Royal Automobile Club, Britain's representative on the world council, said the organisation had no comment.
"These are allegations only and we wouldn't comment on rumour and speculation - and certainly not on people's private lives," she said.
BBC 5 Live motor racing commentator David Croft said he understood the world council had given Mosley its full backing and members had offered their personal support.