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.
Tadic told reporters on Thursday that the arrest was "the result of the new government's commitment to respect international law and laws of the Republic of Serbia, and to bring to justice each individual responsible for crimes in the former Yugoslavia."
Karadzic, 63, accused of crimes against humanity over his role in the 1992-1995 Bosnian war, was captured by Serbia's security service on Monday after more than a decade in hiding. A judge in Belgrade ruled on Tuesday he can be tried at the International Criminal Tribunal for the former Yugoslavia in The Hague.
The speed of his capture after the formation of a new government and appointment of a new security chief reinforced widespread rumors that former nationalist prime minister Vojislav Kostunica had been protecting the war crimes suspect.
Serbia remains under pressure to capture two other war crimes suspects, Bosnian Serb General Ratko Mladic, 66, and Goran Hadzic, 49, wanted for war crimes in Croatia.
Nationalist protests against the former leader's arrest continued in central Belgrade on Wednesday evening, with several hundred people rallying on Republic Square.
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 on Wednesday that once in The Hague, Karadzic will be defending himself.