Karadzic, 63, accused of crimes against humanity over his role in the 1992-1995 Bosnian war, was detained by Serbia's security service on July 21 after more than a decade in hiding. A judge in Belgrade ruled Tuesday that he could be tried at the International Criminal Tribunal for the former Yugoslavia in The Hague.
"Due to the serious nature of the threats, we have taken additional security measures to protect those who may become targets of criminal or terrorist attacks while performing their state or public duties," Milorad Veljovic told the Belgrade-based Tanjug news agency.
Veljovic said police would also investigate all threats received by e-mail addressed to Serbian President Boris Tadic, Interior Minister and Socialist Party leader Ivica Dacic, and other senior state and judicial officials.
Serb nationalists have sharply criticized Tadic and other state officials for collaborating with the West over Karadzic's capture.
The capture, which came only two weeks after Tadic's pro-Western government came to power, has been welcomed by Western countries, and received as an important step in Serbia's drive to join the European Union.
Karadzic is likely to be extradited to the Netherlands within the next few days, to face genocide charges at the Hague tribunal. His lawyer said last week that once in The Hague Karadzic would defend himself.