He did not offer details of the hunt for Mladic, who was charged with genocide for the three-year siege of Sarajevo and for the slaughter of 8,000 Bosnian Muslims in Srebrenica during the 1992-95 Bosnian war.
Hadzic was accused of crimes against humanity during Croatia's 1991-95 war for independence.
Serbian nationalists have issued death threats against Tadic and called him a "traitor" after the arrest of Karadzic on July 21.
They consider Karadzic and Mladic heroes despite their indictments at the UN war crimes tribunal for former Yugoslavia.
Tadic said the threats by some ultranationalist officials go with his job.
|Mladic is charged with the Srebrenica massacre [AFP]
"The liquidation threats, however, are not good for the country and its international image," he said.
"But I'm ready to take the risk."
While vowing to fulfil Serbia's international obligations to the Hague, Tadic also said that he would seek the UN General Assembly's support to challenge Kosovo's unilateral declaration of independence before the International Court of Justice.
On February 17, the ethnic Albanian majority in Kosovo unilaterally proclaimed independence and was promptly recognised by about 40 countries, including the US and most of the European Union nations.
Serbia and its traditional ally Russia immediately rejected the move, considering it illegal and claiming violation of international law.
Stephen Wordsworth, the UK's ambassador in Belgrade, said the motion would not be welcomed by the EU, which Serbia has been trying to join.
"The initiative before the [ICJ] court seems a straight challenge" of the EU by Serbia, Wordsworth was quoted as saying in an interview with the Vecernje Novosti newspaper published on Sunday.
"The process will attract a lot of public attention and it will be difficult to cooperate on [Serbia's] integration into the EU and to confront it at the same time," he said.
"That is why we think it is a mistake," the daily cited him as saying.
The EU and Serbia signed in April the Association and Stabilisation Agreement, considered to be a first step towards full membership in the bloc.
Belgrade hopes to reach the candidate status by the end of the year and eventually to join the EU in 2012.
Meanwhile, Serbian officials said on Saturday that nine people had been detained for clashing with police at a rally in support of Karadzic last Tuesday.
Prosecutors said the nine face charges of endangering public security and committing criminal acts against state institutions.
Officials say about 80 people were injured at the rally in downtown Belgrade when nationalist rioters clashed with police.
Officers fired gas and rubber bullets to disperse them.