Tens of thousands of people have held a rally in the Hungarian capital, Budapest, to protest against the new constitution, which they say harms democracy.
The country's governing Fidesz party pushed the law through parliament in April after winning a two-thirds majority in parliamentary elections.
Opponents say it threatens democracy by removing checks and balances set up in 1989 when Communism fell.
The European Union and US had also asked for the law to be withdrawn.
The dispute has cast doubt over talks on a new financing agreement with the EU and IMF, seen as vital for market confidence in the central European country.
Several centre-left opposition parties joined in the protests, held near a gala event organised by the government to celebrate the new constitution.
Protesters chanted slogans denouncing the centre-right Prime Minister, Viktor Orban, and carried placards denouncing his "dictatorship" as officials arrived for the event.