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.
The former Bosnian Serb leader had assumed a false identity under the name Dragan Dabic to evade capture for years, wearing a long beard and posing as a doctor of alternative medicine.
Government officials say he was captured on July 21, bringing an end to his 13-year status as a fugitive.
But Vujacic says the authorities have not given a true account of what happened.
"They are hiding the truth in their offical explanation when they say he was arrested on July 21," he said.
"It was only on that day he was transferred to the special court. I'm claiming, and we have a lot of evidence, that he was apprehended on the July 18.
"This was kidnapping, this was abduction, this was not being arrested. He was illegally detained."
Vujacic has filed a lawsuit against Karadzic's alleged abductors, and said that Karadzic was asked about the claims by a prosecutor on Friday.
|Identity papers of 'Dragan Dabic', the assumed name of Karadzic [AFP]
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."
A number of demonstrations have taken place in support of Karadzic in Belgrade and Republika Srpska.
Supporters in Pale, the former Bosnian Serb's home town, 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.
Fisher said on Saturday 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".
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.
Prime minister threat
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.