The Mothers of Srebrenica believe the UN was bound to protect them
A Dutch court is considering whether the UN can be sued for failing to prevent the massacre of thousands of Bosnian Muslims at Srebrenica in 1995.
About 6,000 relatives of those killed have brought a case against the UN and the Dutch government over the killings.
Dutch peacekeepers, under a UN flag, failed to intervene as Bosnian Serb forces killed more than 8,000 Muslim men and boys in one week in July 1995.
The enclave had been designated a UN safe haven.
The UN has refused to take part in the case, claiming immunity - a position backed by the Dutch government.
Dutch government lawyer Bert-Jan Houtzagers said the UN must be allowed to operate without facing the threat of prosecution.
"The Bosnian Serbs are the ones who are to blame, especially General [Ratko] Mladic. He is a war criminal," he said.
Gen Mladic led the Bosnian Serb forces that overwhelmed Srebrenica. He has been indicted but is still at large.
But Axel Hagedorn, lawyer for the victims' relatives, said: "Functional immunity does not mean that international organisations are wholly above the law.
"Boundless immunity of the UN is both unacceptable and undesirable for the proper functioning and credibility of the UN."
A number of cases have been brought by small numbers of Srebrenica survivors or relatives - including one by two families which opened in a Dutch court on Monday - but this collective action is distinguished by its size, representing thousands of relatives, including the Mothers of Srebrenica group.
The Srebrenica massacre has been established as genocide, by the International War Crimes Tribunal in The Hague.
The Dutch cabinet resigned in 2002 after a report blamed politicians for sending the Dutch UN troops on an impossible mission.
Now Dutch judges, at The Hague District Court, have to decide whether the UN can be held responsible for the tragedy, under Dutch or international law.
The court will also consider whether the Dutch government can be sued.
After Wednesday's hearing, the court said it would announce its ruling on 10 July.
Many nations are likely to be watching the decision carefully, says the BBC's Nick Miles.
If it opens up the way for the Netherlands to be sued it could make governments more wary of committing troops for peacekeeping operations - making it still harder for the UN to sustain keep them going.