The first trial of a state charged with genocide has opened in The Hague, where Bosnia-Hercegovina will accuse Serbia and Montenegro of war crimes.
Thousands died in the 1992-1995 conflict in Bosnia
Bosnia says Belgrade was responsible for crimes of genocide on its territory during the early 1990s Bosnian war.
Belgrade denies its intention was to wipe out Muslims in eastern Bosnia.
The EU is also exerting pressure on Serbia, as foreign ministers threaten to freeze association talks unless it co-operates over war crimes suspects.
The ministers did not set a specific deadline, but indicated that they wanted fugitive suspect Ratko Mladic handed over by the end of March. He is accused of genocide and other crimes committed during the Bosnia war.
The ministers warned that negotiations with Serbia scheduled for April could be postponed if the former Bosnian Serb general was not surrendered to the UN war crimes tribunal.
Serbia's Deputy Prime Minister Miroljub Labus said the security services had been told to arrest Gen Mladic and he hoped this would happen by the end of March.
The genocide case against Serbia and Montenegro is being heard at the International Court of Justice (ICJ), also in The Hague.
On Monday, hundreds of survivors of the war held a vigil outside the court and read out the names of Bosnian Muslims killed by Serb forces.
The hearings at the ICJ or World Court, which mediates in disputes between states, are scheduled to run until 9 May, but a ruling is not expected until the end of the year.
The BBC's Geraldine Coughlan in The Hague says if Bosnia wins the genocide case, it will seek compensation from Serbia, which could run into billions of dollars.
"The Belgrade authorities have knowingly taken the non-Serbs of Bosnia and Hercegovina on a path to hell, a path littered with dead bodies, broken families, lost youths, lost future, destroyed places of cultural and religious worship," Bosnia lawyer Sakib Softic told the court.
Serbia will deny that the state - rather than a group of individuals - had the specific intent to wipe out the Muslim population of eastern Bosnia.
Bosnia's case will focus on the 1995 Srebrenica massacre, already established as genocide by the International War Crimes Tribunal for the Former Yugoslavia.
Proving the Serbian nation's responsibility for the most serious war crime of genocide is an historic challenge for the Bosnian legal team, the BBC correspondent says.
The hearings have been delayed for more than a decade, since Belgrade filed a series of counter-claims and disputed the court's authority.