Protesters had called last week for him to step down over the accusation.
"In this situation, when my personal issue splits my beloved country instead of uniting it, I feel it is my duty to end my service, and to resign," he told parliament Monday.
Schmitt insisted Monday that his conscience was clear, repeating an assertion he made in an interview aired Friday on public access television station M1.
He said Monday that he was prepared to go to court to prove that he was right.
"I have written my thesis with my best knowledge I had at the time, and I never intended to plagiarize. However, I will accept the decision of the (University) Senate that has withdrawn my doctorate. But this has got nothing to do with me being a president," he said Friday.
Schmitt, a former Olympic fencing champion, wrote his dissertation in 1992 for the University of Physical Education, which is now part of Semmelweis University in Budapest.
In January 2012, the Hungarian HVG weekly reported that a large part of Schmitt's dissertation was copied.
A university investigation also found that large parts of it were plagiarized. A committee said last week that more than 200 pages of the 215-page document showed "partial similarity" to other works or were direct translations.
The university stripped the president of his doctorate Thursday.
"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."
