Tens of thousands protested Monday against Hungary's new constitution, which critics say curbs democracy, while the governing centre-right government celebrated the new law at a gala event.

The demonstration entitled: "There will be a Republic again", was organised by civil groups which claimed nearly 100,000 people gathered on one of Budapest's main avenues.

Critics say the new constitution, which entered into force on January 1, curbs constitutional court powers, threatens media pluralism and ends judicial independence.

Protesters denounced the government of Viktor Orban, with the socialist MSZP, the green-leftist LMP and former prime minister Ferenc Gyurcsany's DK taking part in the rally. Politicians were not allowed to take the stage.

Protesters with boards saying "Enough!", "Orban dictatorship", "Orbanistan" chanted anti-Orban slogans as government dignitaries and President Pal Schmitt arrived to the gala event held in the Opera on the same avenue to celebrate the entering into force of the constitution.

"Viktor Orban and his servants turned Hungary from a promising place to the darkest spot in Europe," Socialist parliamentarian Tibor Szanyi said, calling on people to join in "sweeping out the Orban dictatorship".

Next to the protesters, a group of neo-Nazis held a counter-demonstration to reclaim the street from what they called "the deadly enemies of Hungarians", triggering some scuffles.

The "Fundamental Law", which renames "the Republic of Hungary" to simply "Hungary", was adopted in April thanks to a two-thirds parliamentary majority that enables Orban's government to change legislation at will.

It has drawn fire from the European Union, US Secretary of State Hillary Clinton and Amnesty International.