The EU’s commissioner on enlargement, Olli Rehn, put it bluntly after a meeting of foreign ministers in Brussels when he said: "It's not a grace period but rather a final countdown for the European future of Serbia."
"Serbia has still some weeks to achieve full cooperation with (the UN tribunal), roughly until the end of March," Mr Rehn said.
In a report to EU foreign ministers, Mr Rehn said that Serbia's cooperation with the International Criminal Tribunal for the former Yugoslavia (ICTY) had fallen short of expectations.
The EU ministers said that Serbia and neighbouring Bosnia had to do more to bring fugitives such as Bosnian Serb political leader Radovan Karadzic and military chief Ratko Mladic to justice.
The conflict's most wanted men, Karadzic and Mladic, are still on the run, a decade after the war in Bosnia that claimed 200,000 lives and left more than two million homeless.
Both men have been indicted by the ICTY -- based in The Hague -- for genocide and other crimes, including ordering the Srebrenica massacre of 8,000 Muslims at the end of the 1992-1995 war.
Last year, the EU delayed the start of full membership talks with Croatia, another of the former Yugoslav republics, for not doing enough to help the court find a major suspect, General Ante Gotovina.
Gotovina was arrested in early December after four years on the run.
Landmark case
Meanwhile, a landmark genocide case has opened in the International Court of Justice in The Hague, accusing Serbia of committing genocide against Bosnia's Muslims and Croats.
In their opening statement, lawyers for the Bosnian government accused Serbia of dragging its Muslim and Croat populations along a "path to hell... littered with dead bodies" during the Bosnian conflict.
The Bosnian lawyers compared the 1992-1995 war, which claimed up to 200,000 lives and left millions homeless, to a "man-made tsunami that destroyed the very character of Bosnia-Hercegovina."
The government in Sarajevo is demanding compensation from Serbia and Montenegro via a ruling in its favour by the ICJ, the highest UN court.
Monday's hearing was adjourned after the opening statement.
Bosnia's representative to the court, Sakib Softic, stressed that Sarajevo is not out for revenge, but is determined to set the record straight in the face of Serb denials.
Sarajevo's legal team said it will rely heavily on evidence gathered by prosecutors in cases at the UN war crimes tribunal for the former Yugoslavia.
The hearings will last more than two months. The media is not allowed to report on testimony until all evidence has been heard.
After the case wraps up on May 9, the 16-judge panel will retire to consider its verdict, a process which typically takes months.
Outside the Peace Palace, the seat of the ICJ, dozens of Bosnian Muslim protesters gathered and attached large banners to the fence listing the names of victims of the July 1995 Srebrenica massacre.
"We want justice and the truth to come out," Edina Krdzic, 22, and Edisa Suljic, 21, told AFP.
Ms Krdzic lost her father, two uncles and two cousins in the massacre, while Ms Suljic lost her grandfathers and an uncle.