Anti-government riots left 150 people injured just 24 hours earlier after protestors stormed the state television building in Budapest.
Police used water canon and teargas to disperse the protestors who torched cars and clashed with police.
The violence erupted after a leaked tape revealed Mr Gyurcsany admitted lying about the state of the economy to win an election.
The tape was broadcast on public radio over the weekend giving an insight into his closed-door discussion with his deputies in May.
In the recording, Mr Gyurcsany confessed that his government had accomplished nothing over the past 18 months and that he "lied morning, night and evening" to win re-election in April polls.
"The prime minster confessed he lied about his programme and we want him to resign," said Marton, a 21-year-old business student.
"Hungarian people have had enough," said another student Gergo.
Smaller anti-government protests were also held in cities across Hungary during the day on Tuesday.
Protestors gathered again in front of parliament vowing to march to the headquarters of the state radio broadcaster.
But Mr Gyurcsany defiantly told state television that he would not resign.
"The correct decision is to stay," Mr Gyurcsany said.
In an expletives-laden speech he also vowed a fresh start.
He appealed making to his Socialist MPs to back his austerity package and ambitious economic reforms to stabilize the economy.
Hungary has the highest public deficit in the European Union.
The Prime Minister insisted he will not bow to the protesters and roll back his economic reforms, saying "No, these are my policies."
Conservative opposition leader Viktor Orban earlier demanded that Mr Gyurcsany step down if he loses local elections on October 1.
Orban's Fidesz party was handed a resounding defeat in the legislative vote, giving it a double-digit lead against the Socialists.
Mr Gyurcsany’s party has been weakened by its unpopular reforms including tax rises, mass layoffs and cuts to energy subsidies.
The upcoming elections feature mostly independent candidates and analysts say they are unlikely to hand an uncontestable victory to either party.