"The street is not a solution, but instead causes conflict and crisis," Ferenc Gyurcsany, the prime minister, told state news service MTI on Tuesday.
"I'm staying and I'm doing my job. I'm extremely committed to fulfilling my programme, fiscal adjustments and reforms," he added.
Gyurcsany was speaking hours after angry demonstrators stormed the headquarters of the country's national television station to call for his resignation on Monday night.
The protests were sparked by the leak of a tape in which Gyurcsany admits he had "lied in the morning and lied in the evening" during the government's re-election campaign in April.
Buildings set alight
The demonstrators also set alight buildings and cars in the centre of Budapest in front of the television station on Monday evening.
Rescue services said at least 150 people were injured in the violence, including some police.
150 people were injured in the
clashes, mainly of them police
The authorities had fired tear gas and water cannon at the several hundred-strong crowd of stone-throwing protesters.
The demonstrations are the first such violent protests since the fall of communism over a decade ago.
Gyurcsany said the riots were the country's "longest and darkest night" since the end of communism.
The protesters on Monday night shouted "56" in memory of Hungary's failed uprising against Soviet rule in October 1956.
About 10,000 people had earlier gathered at parliament to demand the resignation of the socialist government.
The protests came two weeks ahead of local elections on October 1 as Gyurcsany's ruling Socialist Party's popularity has fallen to 25 per cent from 40 per cent at the election.
The main Fidesz opposition urged the prime minister to go amid what it called a "moral crisis" while Ibolya David, leader of the smaller opposition Hungarian Democratic Forum, told MTV "the prime minister should abandon public life".