The calls came after Ferenc Gyurcsany acknowledged the authenticity of a leaked audio recording of a speech made during a socialist party meeting in May, in which he said the government had lied to the public about the state of the economy and the need for reforms.
"I will not resign," Gyurcsany told the ATV television station after several thousand protesters gathered outside parliament in Budapest on Sunday night demanding his resignation.
During the meeting held behind closed doors on May 26, one month after the socialists won re-election, Gyurcsany said the government would have no choice but to reform in its second term after what he said were lies that had characterised his 18-month premiership.
"We lied in the morning, we lied in the evening," he said in a speech that was littered with obsceneties, and reffered to his own administration as "boneheaded".
A brief excerpt of the recording was made public on Sunday, first by Hungarian state radio.
Longer excerpts were then later posted on Hungarian news websites, and it was unclear who leaked the recording.
"We lied in the morning, we lied in the evening"
Hungarian prime minister
Gyurcsany even took the step of publishing the tape on his own website only two weeks before municipal elections that the opposition Fidesz party intend to turn into a referendum on the government’s performance.
Political analysts say it is unlikely that the prime minister will step down, but that the scandal will further harm his credibility and his chances of becoming president of the socialist party.
In the past several weeks, Gyurcsany has also admitted that to have a better chance to win April's elections the government covered up the true size of the state budget deficit and passed a law introducing tax cuts now described by the prime minister as a mistake.
The government has also recently announced significant cuts in the number of state employees, as well as new and higher taxes, direct fees for health services.
Student leaders have pledged to mass 10,000 people on the streets of Budapest this week, while trade unions said they would take action in October.