In an interview published on Sunday, Gyurcsany said he still planned to seek his party's chairmanship next year and that the results of next Sunday's municipal elections would not affect his plans.
"Neither the government's actions nor what happens in the party depend on the final outcome," he told Hungary's Vasarnap Reggel newspaper.
"I'm going to fight for these policies and part of it is the modernisation of the Socialist Party."
Between 2,000 to 8,000 people attended a rally on Sunday, a far smaller number than Saturday when up to 40,000 people marched in Budapest demanding that Gyurcsany resign.
Protests began last Sunday, when an audio tape leaked to national radio aired comments by Gyurcsany in which he admitted to lying over the state of the country's economy to get his government elected.
Gyurcsany also linked the country's centre-right opposition to rioting earlier this week that left hundreds of people injured and caused severe damage.
Some have called for an overthrow of the government by force.
"This is not only the tragedy of the Hungarian right but also of Hungarian democracy," he said on Sunday.
While the demonstrations have largely been peaceful, last 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.