"Since the former candidate's doctoral dissertation is based on lengthy literal translations, it does not meet the professional and ethical criteria of the 'dissertation prepared using scientific methods' requirement for obtaining a university doctorate," the university's investigators said in a report.
Prime Minister Viktor Orban said it was up to the president to decide what to do.
"Nobody except him can decide," Orban said in a radio interview Friday.
Schmitt was elected by the parliament for a five-year term in 2010.
Germany's defense minister resigned last year in a similar scandal.
Karl-Theodor Freiherr zu Guttenberg quit all political posts in March 2011, adding that he was "taking the step that I would expect others to take."