Vujacic said that withholding the information was "part of the defence strategy".
However, Serbia's state-run Politika newpaper quoted Vujacic as saying he lodged the motion late on Friday, hoping to stall the handover of his client to the tribunal in The Hague.
He was quoted as saying he had mailed the appeal from a post office, but declined to disclose whether he did it in Belgrade or from elsewhere in Serbia so the document would take longer to reach the court handling Karadzic's extradition.
Proof of postage would be sufficient to prove to the court that Karadzic was mounting a formal appeal.
Karadzic faces 11 charges at the war crimes tribunal, including genocide and conspiracy to commit genocide.
He is alleged to have masterminded the murder of about 8,000 Muslim men and boys in Srebrenica in 1995. The massacre was Europe's worst since World War II.
Alan Fisher, Al Jazeera's correspondent in Belgrade, said Vujacic has been to see Karadzic every day, and there had been a number of demonstrations in Belgrade and Republika Srpska in support of Karadzic.
|Identity papers of 'Dragan Dabic', assumed by Karadzic, but not when going on holiday [AFP]
"Thousands have turned out today in Pale, Karadzic's hometown, walking with black T-shirts and banners in support of him.
Supporters in Pale carried pictures of Karadzic reading "Don't touch," "We are with you," "Serb hero," and "The power of prayer".
Many T-shirts depicted him and his wartime military chief, Ratko Mladic, who is also wanted by the UN war crimes tribunal.
Serbian nationalists continued for a third day on Friday in downtown Belgrade, and demonstrators briefly scuffled with police at the Belgrade City Council building.
Fisher said that in Banja Luka, the de facto capital of the Republika Srpska, people turned out "very much in support of the former president of the territory, and against the Serbian authorities for allowing his arrest to happen".
Evidence has shown that Karadzic had a Croatian passport, and had travelled to Austria and Italy, treating patients for an number of weeks, and also Croatia, on holiday.
"How he managed to do this with a passport not even in his assumed name [Dragan Dabic], nobody is certain," Fisher said.
"Some have said it could have been with help from a higher level in Serbia's government, security services and intelligent agencies, enabling him to get a passport.
"The chief prosecutor has said that anyone who assisted him would also be in line to be charged and could go to prison."
Should the Serb court receive an appeal, a panel of judges will meet to decide on it, Ivana Ramic, a Serbian court spokeswoman, said.
The case will then be turned over to the Serbian government, which issues the final extradition order, she said.
Government officials say that Karadzic was captured on Monday, bringing an end to his 13-year status as a fugitive.
He had assumed a false identity under the name Dragan Dabic, wearing a long beard and posing as a doctor of alternative medicine.
Vujacic insists his client was captured last Friday on a public bus in a Belgrade suburb, before being hooded and transferred to an unknown location where he was kept for three days.
He has filed a lawsuit against Karadzic's alleged abductors, and said that Karadzic was asked about the claims by a prosecutor on Friday.
Karadzic plans to defend himself against the UN genocide charges, Vujacic has said, in the same manner that Slobodan Milosevic, Serbia’s president during the Bosnian war, did.
Vjerica Radeta, a senior official from the Serbian Radical Party, said that Boris Tadic, Serbia's prime minister, could face attacks by nationalists angry over Karadzic's arrest.
"We remind Tadic that treason has never been forgiven in Serbia … Every traitor in Serbian history has met with damnation," he said.
The Democratic Party (DS) and G17 Plus vigorously condemned the remarks from Radeta, calling on the prosecution to react immediately, and launch criminal proceedings against her, claiming she was guilty of jeopardising security.
"It's disgraceful that eight years after the democratic changes in Serbia that anyone should be making such death threats to the president," Zeljko Ivanji, a G17 Plus MP, told Serbia's B92 station.