By Krisztina Than

BUDAPEST (Reuters) - Thousands of Hungarians protested on Sunday against changes to the constitution approved by parliament last week despite domestic and international concern that the move would undermine democracy.

Last Monday parliament, dominated by Prime Minister Viktor Orban's center-right Fidesz party, voted to limit the powers of the constitutional court. This prompted criticism from the European Union, of which Hungary is a member, the United States and human rights groups.

Orban has dismissed arguments that the changes to the constitution are anti-democratic, saying there was no evidence of any breach of EU rules.

But the 3,000 protesters who turned up in central Budapest on Sunday in the freezing cold thought otherwise.

"On March 17, 2013 Hungary is not a dictatorship yet. But there is already an applicant for the job," Laszlo Majtenyi, a former ombudsman and eminent lawyer told the crowd.

"The government has failed us on every level," said Greta Juhasz, a 25-year old student from Budapest. "The constitutional amendments, the economy, but even a freak snow storm proves that they don't deserve to stay in power."

Human rights groups have protested against the changes, saying they enshrine some government measures that had been previously struck down by Hungary's top constitutional court, including a ban on political campaign adverts in private media.

According to the changes, the top court can review the constitution or amendments to it only on procedural grounds, not on substance, and rulings of the court made before 2012 will cease to be in force.

The European institution responsible for defending human rights, the Council of Europe, had urged Budapest to postpone the vote on the changes but Fidesz pushed ahead.

On Thursday European Commission President Jose Manuel Barroso reiterated his concerns to Orban during a meeting in Brussels and said the EU executive would assess the new rules to prepare its response. The U.S. State Department has also expressed concerns.

(Reporting by Krisztina Than and Marton Dunai; Editing by Stephen Powell)