By Mark Lowen
BBC News, Belgrade
Mr Hadzic and Gen Mladic are believed to be hiding somewhere in Serbia
The UN's chief war crimes prosecutor has said Serbia's co-operation with the International Criminal Tribunal for the former Yugoslavia is "progressing".
However, in his report to the UN, Serge Brammertz said Serbia must continue searching for two fugitives.
They are Bosnian-Serb military leader Ratko Mladic and Goran Hadzic, who is wanted for war crimes in Croatia.
Belgrade hopes the largely positive report will help unblock Serbia's European Union hopes.
These were frozen last year by the Dutch government demanding that the fugitives be caught.
The Serbian government has been waiting with bated breath for this latest report, eager for the chief prosecutor to make a favourable assessment of Belgrade's performance.
In the end, Mr Brammertz's conclusions were the most positive to date but he noted that Serbia must pursue its attempts to find the two remaining fugitives, who were indicted for war crimes during the 1990s.
In the report, Mr Brammertz said: "Serbia's co-operation with my office has continued to progress.
"Prosecution requests to access documents and archives are being dealt with more expeditiously and effectively... Serbia must maintain these efforts with the clear objective of apprehending the fugitives."
Crucially, the magic words "full co-operation" were not uttered.
That is the phrase that the Netherlands had demanded in order to unfreeze the Interim Trade Agreement - a precursor to Serbia's longed-for EU membership negotiations.
The Dutch government froze the agreement last year, demanding that Serbia prove its commitment to catching the fugitives.
However, Belgrade - and many in Brussels - believe that Serbia's significant progress in its co-operation with the tribunal may now persuade the Dutch to unblock the agreement as early as next week.
This would pave the way for Serbia's formal application for EU membership by the end of the year.
Responding to the report, the Serbian President Boris Tadic said his government is doing everything in its power to locate the two indictees.
It will now be up to the EU foreign ministers meeting on Monday to decide whether to reward Serbia for progress made or maintain pressure on Belgrade, by keeping the door to the EU firmly locked.