Alan Fisher, Al Jazeera's correspondent in Belgrade, said: "There are people of all ages. I would estimate that there are between 15,000 and 20,000 people.
"The people in [Republic] square are listening to speaker after speaker... every time Karadzic's name is mentioned there is a huge round of applause.
"I'm sure that the party that organised this and Karadzic's family will be pleased with the turnout."
'Symbol of resistance'
The right-wing Serbian Radical party, which organised the rally, said it had brought in Karadzic supporters by bus from all over Serbia and Bosnia, where Karadzic is still revered by many as a wartime hero.
"This rally will be a symbol of resistance, a symbol of the strength of those who love freedom more than anything," Aleksandar Vucic of the nationalist Radical Party said.
"We'll continue resisting dictatorship in Serbia, we'll continue raising the question of whose paramilitary forces arrested Radovan Karadzic, how and why."
Many protesters chanted slogans against Boris Tadic, Serbia's president, who warned the protesters to remain peaceful.
"Everyone has the right to demonstrate, but they should know that law and order will be respected," he said.
In February, when the ultra-nationalists organised a rally against Western countries that recognised Kosovo's independence, the US embassy was partly burned and protesters looted and smashed shops and McDonald's restaurants in Belgrade.
Karadzic is in a Belgrade jail awaiting extradition to the UN war crimes court in The Hague, indicted over the Srebrenica massacre, which left about 8,000 Muslim men and boys dead, and the the siege of Sarajevo, during which more than 11,000 people died.
Court awaits appeal
Karadzic's lawyer has said that he had sent an appeal against his client's extradition to a Belgrade court by registered mail on Friday, but on Tuesday, officials confirmed it had still not arrived, while the postal service also said it did not have the document.
"The law is not specific on how long the court should wait [for the appeal to arrive]," Svetozar Vujacic, Karadzic's lawyer in Serbia, said on Tuesday.
|Many demonstrators sang nationalist songs during Tuesday's protest [Reuters]
"It is also not written in the law where the appeal may be sent from. Widely interpreted, it could be from Sydney, although of course I did not actually send it from Sydney."
He said he may have sent the appeal letter from Bosnia, and expected it to arrive in Belgrade "in seven days at the earliest".
A court spokeswoman said that the court had not yet decided whether it would wait longer for the document, or rule that the deadline had passed, and go ahead with the extradition.
Officials say the war crimes suspect was captured on July 21 in Belgrade, where he lived under the assumed identity of a health guru, with a long white beard and hair, and large glasses.
His lawyer claims that Karadzic was kidnapped on a Belgrade public bus on July 18, and illegally held for three days by unknown captors.
Serbia's new, pro-Western government hopes that Karadzic's arrest will strengthen the country's bid for EU membership.
Serbia had been accused of not searching for war crimes fugitives sought by the UN tribunal.