Nationalists have labelled President Tadic a "traitor"
Serbian President Boris Tadic has said Belgrade will fulfil its international obligations to arrest remaining war crime suspects wanted by a UN tribunal.
It was the first time Mr Tadic had spoke on the issue since the arrest and extradition last month of the former Bosnian Serb leader, Radovan Karadzic.
He vowed to track down Mr Karadzic's military commander, Ratko Mladic, and ex-Croatian Serb leader Goran Hadzic.
They are wanted for their alleged role in war crimes during the Bosnian war.
At a press conference, Mr Tadic said his country would co-operate fully with the UN war crimes tribunal in The Hague, and that there was no need for any "additional pressure".
"All those who have the idea to put additional pressure on Serbia are knocking on open doors, because not only has Serbia shown its will and determination but it also has made concrete steps related to this co-operation," he told reporters.
Eleven counts of genocide, war crimes, crimes against humanity and other atrocities
Charged over shelling Sarajevo during the city's siege, in which some 12,000 civilians died
Allegedly organised the massacre of up to 8,000 Bosniak men and youths in Srebrenica
Targeted Bosniak and Croat political leaders, intellectuals and professionals
Unlawfully deported and transferred civilians because of national or religious identity
Destroyed homes, businesses and sacred sites
The arrest of Mr Karadzic, 63, and other indicted war criminals is one of the main conditions of Serbian progress towards joining the European Union.
Mr Tadic said: "Today nobody can tell Serbia it is avoiding international justice and it does not respect international law."
He praised Serbia's security forces for "doing their job". His comments come despite death threats by nationalists, who have denounced Mr Tadic as "a traitor".
Radovan Karadzic was arrested in Belgrade on 21 July after more than a decade on the run, and was extradited to the International Criminal Tribunal for the former Yugoslavia (ICTY).
He faces 11 counts of war crimes including genocide for his alleged role during the Bosnian conflict of the early 1990s.
The UN says Mr Karadzic's forces killed up to 8,000 Bosniak men and boys from Srebrenica in July 1995 as part of a campaign to "terrorise and demoralise the Bosnian Muslim and Bosnian Croat population".
He has also been charged over the shelling of Sarajevo, and the use of 284 UN peacekeepers as human shields in May and June 1995.
Mr Karadzic has denied the charges against him and refused to recognise the legitimacy of the UN tribunal.
Serbian officials said details of Mr Karadzic's capture were being withheld, as the authorities were planning to use "operational data" to track the two main war crimes suspects still at large, Gen Mladic and Goran Hadzic.