Vujacic told Al Jazeera on Sunday that he had mailed an appeal against Karadzic's extradition to The Hague at the last possible moment late on Friday, in order to delay the process.
The war crimes court in Belgrade, the Serbian capital, which is dealing with the case of the former Bosnian Serb wartime leader, said on Monday that the appeal had not arrived by the start of morning office hours.
Speaking on Monday, Vujacic said: "That is the defence team's strategy and I can't talk about this now, because if I said to you when or from which post I lodged the appeal on Friday, be sure that the appeal would have been rejected on Friday night and Radovan Karadzic would have been extradited to The Hague the next morning."
Karadzic faces 11 charges at the UN tribunal, including conspiracy to commit genocide.
He is accused of instigating the 1995 slaughter of 8,000 Muslim men and boys in Srebrenica and the three-and-a-half year siege of Sarajevo, which left 10,000 people dead.
Officials say the war crimes suspect was captured a week ago in Belgrade, where he lived under an assumed identity.
His lawyer claims that Karadzic was kidnapped on July 18 and held for three days by unknown captors.
|Luka Karadzic and his sister Ivanka visited Karadzic in prison [AFP]
Once Serb judges decide on the appeal, which they are likely to reject, the case will be handed over to the Serbian government, which issues the final extradition order.
Also on Monday, Dragan Karadzic, Radovan Karadzic's nephew, was filmed going into his uncle's prison with a suit, food, books and cookies.
Some residents of the Serbian capital have expressed hope that Karadzic's extradition would be dealt with quickly, while others have questioned whether the move to extradite Karadzic is necessary.
"The sooner the better," Sevda Darskarvic said.
"We need to finish with him because we have a lot of other problems and more important ones than his extradition," she said.
Militsa Korngaca, a Belgrade resident, said: "I'm not a big fan of The Hague tribunal. If we have to judge him it should be done here in Bosnia."
There are fears of violence on Belgrade's streets on Tuesday evening with ultra-nationalists trying to prevent Karadzic's extradition by force.