The former Bosnian Serb leader is currently in a prison in the capital awaiting extradition to the war crimes tribunal, which may go ahead sometime this weekend.
However, Vujacic said he would formally appeal against Karadzic's extradition order on Friday, when a legal deadline expires, in order to allow his family to visit if they are allowed to leave Bosnia.
Vujacic said that Karadzic had asked for and got a haircut and shave in prison on Wednesday and that "he looks like his old self, a bit aged".
Reporting from the area where Karadzic had been living when he was captured, Nick Clark, Al Jazeera's correspondent in Belgrade, said: "There's complete disbelief that he lived for such a time under their noses without anyone realising."
Clark said that generational differences were in play with regard to how people were reacting to news of the arrest.
He said: Amongst the older generation it is not difficult to find strident nationalist views. Younger people on the street are not so passionate."
Clark said that there were concerns that a friendly match being played between Partisan Belgrade and French club Lyon in the capital on Wednesday might be hijacked by nationalist supporters of Karadzic.
He said: "Police are saying hundered if not thousands of nationalists may attend the game. US citizens have been told to stay indoors... last time there were nationalist demonstrations their embassy was torched."
Karadzic's wife and children are banned from leaving Bosnia under measures targeted at Karadzic's support network.
On Tuesday evening, Milorad Dodik, the Bosnian Serb prime minister, promised to financially assist the family. Because of the restrictions, the government had previously been unable to help the family in case the funds would aid Karadzic.
Speaking on Wednesday, Karadzic's daughter said she was grateful for the help offered to her family by government and hoped it would allow them to stabilise their lives after a very difficult decade.
"I am grateful to Mr Dodik for understanding our situation and I hope he will really help us to normalize our lives and solve the enormous problems we have," Sonja Karadzic said
She also appealed to the government to allow her family to visit her father.
"These gentlemen know about our situation and I appeal upon them to allow us this visit. After 10 years of hell, I do not how anybody can benefit from additionally mistreating us," she said.
Meanwhile, Karadzic's brother, Luka, said that Karadzic had "planned to turn himself in January 2009 because that is when The Hague tribunal is due to stop launching new trials. It would be more fair if he could be tried in Serbia with the presence of an international judge".
The EU has called Karadzic's arrest "a milestone" on Serbia's road to joining the EU but said Belgrade must go further to reap the full benefits, by arresting Ratko Mladic, Karadzic's military chief, who is wanted on the same charges.
Inside Serbia, the reaction to the arrest has been muted.
|Karadzic is accused of genocide over the Srbrenica massacre [EPA]
Government ministers have kept quiet, fearing a backlash from hardline nationalists who see Karadzic and Mladic as heroes.
"All true Serbs know what Radovan Karadzic stands for," the fringe group Obraz (Dignity) said in a statement.
"If Serbia's enemies and their servants here think they have destroyed his legend, they are very wrong. We are all Radovan."
Among the main nationalist parties, reaction has been limited to fiery rhetoric about betrayal.
There have only been a few small street protests in Belgrade and ordinary people seem to be weighing the benefits of closer EU ties against national pride.
Karadzic faces two indictments, one for genocide for the massacre of 8,000 Bosnian Muslims in the town of Srebrenica in 1995 and the second for the 43-month siege of Sarajevo.
About 11,000 people died in the city from sniper fire, mortar attacks, starvation and illness.