Mr Hadzic and Gen Mladic are believed to be hiding somewhere in Serbia
Serbian President Boris Tadic has told the UN's chief war crimes prosecutor his country is "searching intensively" for two remaining fugitives.
Serge Brammertz is visiting Serbia to assess its hunt for former Bosnian Serb army chief Ratko Mladic and the former Croatian Serb leader, Goran Hadzic.
Earlier, a minister said they could be tracked down by the end of the year.
Serbia's passage to membership of the EU has been held up until it is judged to be co-operating with the tribunal.
Mr Brammertz, the chief prosecutor for the International Criminal Tribunal for the former Yugoslavia (ICTY), arrived in Belgrade on Monday for a two-day visit, during which he will assess the Serbian authorities' level of co-operation.
At a meeting with President Tadic and Rasim Ljajic, the minister in charge of dealing with the ICTY, he was briefed on the latest actions undertaken in an effort to capture the tribunal's two remaining fugitives.
The prosecutor was told "that Serbia has been intensively searching for the remaining fugitives", the office of the president said.
Earlier, Mr Ljajic said he was confident that Gen Mladic and Mr Hadzic "could not hide forever".
"If they were in Serbia, it would be impossible not to find them before the end of the year," he told Serbian newspaper, Blic.
The Serbian government has said this is the most important visit so far by the chief prosecutor of the ICTY.
It comes at a crucial time for the former Yugoslav republic, the BBC's Helen Fawkes in Belgrade says - a decision on whether to allow Serbs to travel without a visa to EU states could be made next month.
"Serbia is still in some ways a pariah nation because Mladic has not been arrested," political commentator Ljiljana Smajlovic told the BBC.
Mr Brammertz will present a report to the UN Security Council in June
"If Brammertz comes and says these people have really helped us, this may make it easier for people in the European Commission and for people in the Council of Ministers to give the green light to Serbia for Serbs to be able to travel without visas," she added.
While Serbian officials believe the visa regime will change soon, they have repeatedly been told that until Gen Mladic and Mr Hadzic are caught, it will not be able to move towards EU membership.
The arrest in July of the former Bosnian Serb leader, Radovan Karadzic, led to claims by some officials that Gen Mladic would be next. But there has since been no arrest.
Gen Mladic was indicted by the ICTY in 1995 on 15 counts of genocide, war crimes and crimes against humanity in Bosnia-Hercegovina between 1992 and 1995 - including the massacre of at least 7,500 Bosniak (Bosnian Muslim) men and boys from Srebrenica.
Mr Hadzic was a central figure in the self-proclaimed Serb republic of Krajina from 1992 to 1993. In 2004, he was indicted on 14 counts of war crimes and crimes against humanity for involvement in atrocities committed by Serb troops in Croatia between 1991 and 1995.
Mr Karadzic is currently on trial at The Hague on 11 charges of genocide, war crimes and crimes against humanity.