Thousands protest against Hungarian PM Gyurcsany

(Adds opposition rally)

BUDAPEST, Oct 23 (Reuters) - Tens of thousands of protesters took to the streets of Budapest on Tuesday to demand Hungarian Prime Minister Ferenc Gyurcsany quit during ceremonies to celebrate Hungary's 1956 uprising against Soviet rule.

The protests organised by the main opposition Fidesz party and by far-right groups were noisy but peaceful after clashes on Monday in which 19 people were injured as rioters hurled petrol bombs and overturned cars.

But with far-right groups mingling with the Fidesz rally, estimated by the police at 30,000, which is marching through the centre of Budapest, police were on the alert for more violence.

Fidesz accused the Socialist government of fomenting the clashes.

"We have assembled here today to show those in power that we cannot be held in fear," Fidesz leader Viktor Orban said.

The protests were a hang over from weeks of violent demonstrations last year following the leaking of a tape in which Gyurcsany, a Socialist, admitted he had lied about the poor state of the economy to win re-election in 2006.

Fidesz said the 47-year-old Gyurcsany, a former leader of the communist youth movement, had betrayed Hungarian democracy and was failing to defend Hungary against a resurgent Russia, which supplies the country with 70 percent of its gas.

"The world is beginning to realize that it's not the revival of communist ideas which represent the challenge... the historic challenge for the West is represented by the growing powers of the new eastern order. We can already feel its presence, breath, radiation in our skin," Orban said.

Gyurcsany has cordial relations with Russian President Vladimir Putin and Russian companies have been on a spending spree in Hungary, most recently buying state airline Malev.

The official ceremonies at Parliament earlier in the day were once again surrounded by barriers and a heavy police presence, triggering renewed anger among those protesting.

"What they are doing is antidemocratic, the Hungarian people cannot celebrate their own national holiday because they close the square off hermitically because... he (Gyurcsany) is afraid of people telling the truth," said Zsolt Molnar, a protester.

While the popularity of the Socialists has plunged to 20 percent from the more than 40 percent they won in the April 2006 election, the demonstrations pose no threat to Gyurcsany, who is implementing economic reforms to rein in a huge budget deficit.

Additional reporting by Sandor Peto and Andras Gergely