Labeled a "March of Peace" the demonstration was by far the largest rally since the government took power in May 2010, in what analysts said was a reminder that Prime Minister Viktor Orban's Fidesz party remains a potent political force.

Orban's center-right government, accused by Brussels of threatening the independence of the media, judiciary and central bank, backed down earlier this week, aiming to prop up its battered forint currency and keep access to financial markets.

The government has said it will work out details of necessary legal changes by Monday after the European Commission started infringement procedures in the three areas, saying Budapest's new laws failed to comply with EU rules.

Orban is travelling to Brussels Tuesday to try to hammer out a political agreement with EU Commission President Jose Manuel Barroso, in order to be able to start formal talks with the EU and International Monetary Fund about a loan deal.

Amid the diplomatic wrangle and market swings the government has also seen its popular support dwindle and big demonstrations against its policies have become regular.

According to a fresh opinion poll, 84 percent of people think things are going in the wrong direction, although the opposition is fragmented and Fidesz still commands the support of about 1.5 million voters in the country of 10 million.

"Those who are here, many of us also think things are not going in a good direction," Bela Petrik, a 22-year-old economy student from Budapest, said at Budapest's Heroes Square as people gathered for a march to parliament.

"But these mistakes should not lead to speculative attacks that serve the interests of nobody except the speculators."