Montezemolo has been highly critical of the new shape of the pinnacle of motor sport, and has reportedly written a letter to Bernie Ecclestone asking for a meeting with all the major stakeholders to discuss the future.
But it is believed Ferrari's highly critical stance was discussed at length during the F1 Commission meeting on Wednesday, and two days later Montezemolo is now tempering his earlier remarks.
"A letter to Ecclestone? I don't need to write to him to arrange a meeting," multiple Italian publications on Friday quoted Montezemolo, 66, as saying at a Maserati event in Modena.
"I never said that Ferrari would pull out, but I do think the time has come to make a reflection on our system. I think Ferrari has the duty to seek improvements for the benefit of the teams, the fans, the media and the sponsors.
"And I think that, having been in formula one for 64 years, Ferrari has the right to think about the future," he added.
"Formula one is an extraordinary sport," said Montezemolo, "but we need to do something to make it better."