The protesters had rallied for a peaceful protest around the opposition Serbian Progressive Party (SNS), a nationalist party.
Tomislav Nikolić, SNS leader, said that unless the deadline was honoured, he would call protests in the capital again until the demands were met.
Parliamentary elections are scheduled for 2012 in Serbia but the opposition wants them held sooner.
Rising prices, unemployment and poverty has led to discontent with Serbia's pro-European Union government, Voice of America reported.
Nikolić accused Serbia's ruling pro-European bloc of hindering change in Serbia and allowing the proliferation of corruption and crime. He urged protesters to help bring about peaceful and dignified changes in the government to prevent the country from further slipping.
Tomislav Nikolić, once a hard-line nationalist, endorsed the prospect of his country's EU accession two years ago, by abandoning his opposition to a Stabilisation and Association Agreement (SAA), the legal basis of Serbia-EU relations (see 'Background').
Aleksandar Vučić, deputy president of SNS, said that the demonstrators had not assembled to "badmouth" either Serbian President Boris Tadić, Economy Minister Mladjan Dinkić or Interior Minister Ivica Dačić, but to tell them clearly and openly that they wanted elections.
Velimir Ilić, leader of opposition party New Serbia, told the crowd that "Serbia wants a new leader," while Nikolić advised Tadić not to "play games with Serbia". He also said that the protesters had not come to create either a new Tunisia or Egypt, but a democratic Serbia, to which the crowd chanted: "Elections, elections." According to police sources, 55,000 protesters were present when the rally began. Vučić told the Serbian Broadcasting Corporation that over 100,000 people participated in the demonstration.