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Mosley was given a strong vote of confidence to remain president of the International Automobile Federation (FIA) on Tuesday, gaining 103 votes to 55 against in a secret ballot at an extraordinary meeting of the general assembly in Paris.
The 68-year-old has ignored calls to quit since March when Britain's News of the World newspaper published details and photographs of his involvement in what was described as a Nazi-style sado-masochistic orgy with prostitutes.
Montezemolo was quoted on Wednesday as saying Mosley "should realise that sometimes it is necessary to say to yourself I have to leave for reasons of credibility".
However, F1 world champions Ferrari issued a statement on Thursday in which Montezemolo clarified his stance.
"I am happy Max Mosley has been confirmed as president of the FIA, through the years he has done an excellent job for Formula One," he said.
"With regards his future, it will only be up to him to decide if and when to take a step back."
Mosley, whose father Oswald was the founder of the pre-World War Two British Union of Fascists, has denied any Nazi connotations to the scandal and is taking legal action against the News of the World for invasion of privacy.
