Several EU members say Belgrade must hand over the men before it can join the bloc.
The most notable fugitive is Ratko Mladic, the former Bosnian Serb military commander, who is wanted by the International Criminal Tribunal for the former Yugoslavia on charges of genocide.
Serb authorities failure to track down Mladic, who is accused of playing a part in the 1995 Srebrenica massacre, prompted the Netherlands to block a key trade accord which was a step on the path to EU membership.
It only recently reversed this decision, allowing the Serbian application to move forward.
The issue of Kosovo, which unilaterally declared independence from Serbia in 2008, is another major stumbling block for Belgrade's ambitions.
Serbia still officially considers Kosovo its southern province, but the territory has been recognised by all but five EU member states.
Despite being aware that membership will not be straightforward, Serbia has been upbeat on the issue and has said the prospect of joining the EU would provide fresh impetus to push through necessary changes.
"The process of accession gives a strong momentum to complete political and economic reforms in Serbia," the government said in a memorandum to accompany the application.
"We say and confirm for the first time on record that we are ready to accept all values and fulfil all obligations that require the transformation of a society wishing to join the EU", said Milica Delevic, head of the Serbian Office for European Integration.
If Serbia does join the EU, an entry date is expected some time between 2014 and 2018.