War crimes prosecutor Carla del Ponte has urged the Serbian authorities to arrest fugitive Bosnian Serb General Ratko Mladic by mid-December.
Ratko Mladic commanded forces responsible for "ethnic cleansing"
The new deadline for his capture was announced after talks in Belgrade between Ms del Ponte and Serb leaders.
Gen Mladic, on the run since 1995, has been charged with genocide and other crimes over the Bosnian war.
The Dayton peace accords which ended the war were signed in Paris on 14 December, 1995.
Ms del Ponte voiced dismay at Belgrade's failure to arrest Gen Mladic in time for the 11 July anniversary of the Srebrenica massacre.
He is accused of orchestrating the killing of nearly 8,000 Muslim men and boys at Srebrenica - the worst single atrocity in Europe since World War II.
"My disappointment - my big disappointment - is because six fugitives are still at large, most probably in Serbia, and that includes, of course, Mladic," Ms del Ponte said.
She believes Gen Mladic is being sheltered by elements linked to the Serb military.
"Now we have another deadline. It will be the Dayton accord in December," she said.
But she added that she was "very pleased with the co-operation we receive from Belgrade, particularly in the transfer of 16 fugitives since October last year".
The BBC's South-East Europe analyst Gabriel Partos says Ms del Ponte's praise for Serbia's co-operation removed any lingering doubts about whether the EU was ready to open talks on a Stabilisation and Association Agreement (SAA) with Belgrade.
As she made her remarks on Thursday, ambassadors of the 25 EU countries in Brussels were giving their approval to a negotiating framework, which will be endorsed by the EU foreign ministers on Monday.
Ms del Ponte will also visit Croatia on Friday, to assess its co-operation with the tribunal in The Hague.
EU foreign ministers are to decide on Monday whether to open EU accession talks with Croatia.
The negotiations have been held up since March by Zagreb's failure to demonstrate full co-operation with the tribunal over the case of the fugitive war crimes suspect, General Ante Gotovina.
Before Ms del Ponte's talks in Belgrade the Serbian foreign minister called for Gen Mladic's arrest.
Vuk Draskovic told the Associated Press that the failure to catch Gen Mladic was jeopardising Serbia's bid for closer ties with the European Union and Nato and its position in forthcoming talks on Kosovo's status.