The protesters’ ranks were swelled by marchers who had planned to attend a political rally by Fidesz, the country’s main opposition party, on Sunday, before it was postponed due to security concerns.
Hundreds of police, most in riot gear with helmets and shields were stationed nearby for but the event in Budapest’s main square passed off mostly peacefully.
Previous protests against the prime minister have turned violent. Clashes between demonstrators and police injuring more than 200 people in total in the past week.
The protests began last Monday after a tape was aired on local media outlets in which Ference Gyurcsany, the Hungarian prime minister, said his government had lied about the state of the country’s economy to win elections in April.
He has rejected protesters’ calls to step down and vowed to push ahead with tough economic reforms.
One protester told AP news agency that he and his wife were marching because they were “embittered that such a man is leading the country”.
“We’ll do anything we can to make him resign,” he said.
Protesters have vowed to continue demonstrating after nationwide municipal elections on October 1, in which Gyurcsany’s Socialist party-led coalition is expected to suffer heavy losses.
One of the key speakers at Saturday’s protest, Laszlo Toekes, a Protestant bishop whose protest sparked the country’s anti-communist Romanian revolution in 1989, said that Gyurcsany was a greater criminal than the protesters who rioted last week.
“Who is really guilty – he who sets a car on fire, or he who destroys a whole nation?” he told the crowd.
Although most demonstrators have marched peacefully, on Monday between 1,000 and 2,000 people fought pitched battles in Budapest’s streets, torching cars and storming the city’s state television building.
The violence has left hundreds injured and up to 150 people have been arrested.