Riot police with shields, helmets, bullet-proof vests and gas masks formed a security cordon around the building as demonstrators, mostly aged in their 20s, continued to pile into the square.
The atmosphere, which began relatively peacefully, turned acrimonious with vitriolic speeches slamming Mr Gyurcsany, who on Monday admitted he had lied to the country about the dire state of the economy to win re-election in April.
"Resign, resign," chanted the crowd as people waved the Hungarian flag as well as the red-and-white flag used by the pro-Nazi Hungarian regime during World War II.
There was, however, none of the violence of previous evenings when more than 200 people were injured and almost 100 arrested in clashes with police during similar protests overnight Monday and Tuesday.
But tension was nevertheless high as police sirens wailed around the streets.
Bomb hoaxes
Both the private HIR TV television channel and the national MTV channel were partially evacuated following two bomb hoaxes.
"An unidentified person called a free-phone number at about 8:00 pm (1800 GMT) and said he was going to blow up the (MTV) building at midnight," a police spokesman said.
The MTV building was ransacked by rampaging protestors on Monday in the worst street protests to hit Hungary since the fall of communism in 1989.
Turmoil broke out after public radio at the weekend broadcast a leaked discussion between Mr Gyurcsany and his deputies in May, in which the prime minister admitted that he had lied ahead of the election.
In a passionate speech peppered with the expletives and blunt talk for which he is well known, the charismatic 44-year-old admitted "we screwed up".
"Not a little, big time. No country in Europe has committed blunders like we have. There is an explanation for this. We obviously lied our way through the past one-and-a-half to two years," he said on the tape.
Fearing the protests could continue to swell, Mr Gyurcsany issued a rare joint statement with President Laszlo Solyom on Wednesday warning against further large-scale rallies.
"In light of the violent events of yesterday evening and this dawn, the organisers of every mass event should consider their own ability as well as that of the police to guarantee security and that participants do not cross the line of legality," the statement said.
Hungarian police said the violence was orchestrated by a small number of radical right-wingers who had hijacked the demonstrations along with a contingent of known soccer hooligans.
Mr Gyurcsany stressed that the riots must stop and that he would not cede to calls for his resignation.
"The government will hold firm on the only track possible: the policies of reform to ensure development and economic stability," the Socialist Party leader told a meeting.
The right-wing opposition Fidesz Party, which is currently riding high in the opinion polls, said Mr Gyurcsany should quit office before local elections due October 1.
Fidesz is expecting hundreds of thousands of supporters to turn out for an opposition rally on Saturday, originally planned as a campaign closing event ahead of the municipal elections.