'If you wish the agreement we made to have any chance of survival, you and Fota must immediately rectify your actions,' wrote Mr Mosley, whose father was the leader of Britain's pre-World War Two Fascist party.
'You must correct the false statements which have been made and make no further such statements. You yourself must issue a suitable correction and apology at your press conference this afternoon.' The letter was sent before Ms Montezemolo and team bosses met in Bologna on Thursday. A Ferrari spokesman had no comment on the letter.
Mr Mosley, who survived calls for his resignation after a sex scandal last year, has traded insults with teams as the sport's crisis came to a head.
At last weekend's British Grand Prix, he labelled some of the team bosses 'loonies' (lunatics) and suggested Renault's Flavio Briatore was after Formula One supremo Bernie Ecclestone's job.
Mr Mosley said in the letter that he had a long-standing plan not to seek re-election but now considered his options open given the 'deliberate attempt to mislead the media.
'At least until October, I am president of the FIA with the full authority of that office,' he added. 'After that it is the FIA member clubs, not you or Fota, who will decide on the future leadership of the FIA.'
Fota vice-chairman John Howett, president of Toyota motorsport, said in Bologna that the teams wanted Mosley's successor to be more independent - a view that would act against Former Ferrari team boss Jean Todt. -- REUTERS