Witnesses said tens of thousands of protesters demonstrated outside of the city's opera house for nearly five hours Monday as Orban and other officials attended a gala inside, CNN reported Tuesday.
Orban and other officials left the gala marking the new constitution through the rear to avoid the crowd, witnesses said.
The new constitution, effective Sunday, omits "republic" from Hungary's official name and includes several paragraphs Amnesty International said violate international human rights. The organization has been critical of constitutional language that defines life as beginning at conception and marriage as being between a man and a woman.
Amnesty International also expressed concern about the possibility of life imprisonment without parole and the lack of language forbidding discrimination based on sexual orientation, CNN said.
U.S. Secretary of State Hillary Clinton had voiced similar concerns last year, urging Orban to commit to an independent judiciary, a free press and a transparent government.
Critics have called the new media law restrictive and said the new election law favors Orban's ruling party. Critics also ripped a law that criminalizes homelessness.