Ferenc Gyurcsany was speaking shortly before thousands of protesters held a second night of demonstrations to demand his resignation on Tuesday evening.
In the centre of Budapest, the Hungarian capital, the protests turned violent after hundreds of bottled-hurling demonstrators skirmished with over 1,000 policemen.
Over 50 people were reported to have been injured in the violence. More than 150 people were injured in similar protests the previous night.
Elsewhere in the city around 10,000 people demonstrated peacefully to call on Gyurcsany to resign, even though the Hungarian leader's had delivered a defiant speech on national television only hours earlier.
"I had spent three minutes on Sunday night thinking about whether I should step down or whether I had a reason to step down, and the conclusion I came to is that absolutely not," Gyurcsany, a business tycoon turned politician, said on national television on Tuesday afternoon.
The riots started when a leaked tape aired on Sunday, in which Gyurcsany said that he and his Socialist party had lied for four years about Hungary's budget in order to win a general election in April.
Higher taxes and fees for healthcare and university tuition had prompted protests before but the release of the tape sparked a violent backlash.
Thousands gathered again at parliament on Tuesday - though there were no reports of violence - and there are also plans for a big student demonstration on Thursday, in which the organisers fear that could be hijacked by far-right parties.
The main Fidesz opposition urged the prime minister to go amid what it called a "moral crisis".
"A pathological liar can not step over his shadow," Viktor Orban, the Fidesz leader told said on Tuesday.
The prime minister has said his taped comments to party members were intended to force them to admit to their mistakes and a wake up call to back much needed reform measures.
Analysts said Gyurcsany was likely to hang on for now, but said the uproar could ultimately cost him his job.
"It will be very difficult for him to survive, not because his own party will back out, but because morality is a factor that's gaining importance in Hungarian politics," said Ervin Csizmadia, an analyst with the Hungarian Academy of Sciences.
“It's hard for me to imagine that it won't create a difficult, unsolvable problem in the medium term, especially as half of Hungary has completely lost its trust in him."
He won April's election partly on a promise of tax cuts but has since imposed tax hikes and benefit cuts worth $4.6 billion in 2007 alone to curb Hungary's budget deficit which will surge to 10 per cent of gross domestic product this year.
Investors who hold billions of dollars of Hungarian bonds are worried over the fate of the reforms, which most economists see as the only way to rescue the country's strained finances and keep up hopes of joining the euro zone.