Mercedes, along with tyre supplier Pirelli, have been summoned to the FIA's headquarters in Paris on June 20 to face an International Tribunal for an apparent breach of the sporting regulations.
The hearing follows a protest launched by Red Bull and Ferrari into Mercedes' use of a 2013 car to assist Pirelli in a 1,000-kilometre test at Barcelona's Circuit de Catalunya from May 15-17.
As a pre-cursor to the event, Di Montezemolo has turned the screw on Mercedes and applied a degree of pressure on the FIA with his latest remarks.
Speaking at the opening ceremony of the new Ferrari museum at the team's headquarters in Maranello, Di Montezemolo said: "We have faith in the FIA.
"I do not wish to comment, but I note with satisfaction that the Federation is following this incident well.
"Let's hope Formula One can maintain its professionalism and we have faith that those who attempt to circumvent the regulations are pursued and prosecuted, or rather more prosecuted than pursued."
A wide-range of sanctions are available to the tribunal should they determine Mercedes guilty, including a fine, points deduction, race ban, or even exclusion from the championship.
The FIA has announced a decision on the case "will be published as soon as possible after the hearing".