But lawyers for the families said on Wednesday there was nowhere else to turn for a fair hearing of grievances.
Axel Hagedorn, whose firm says it represents 6,000 family members of victims in the unusual class-action suit, said he believed the UN's immunity is not applicable in a genocide case.
"They may be responsible but unable to be called to account because of immunity," he said.
"This is unacceptable legally, humanly and morally."
The court said it will rule on the bid by the Dutch state to uphold the UN's immunity on July 10.
The Mothers of Srebrenica, relatives of the men and boys killed, are the most vocal claimants in the civil suit seeking compensation from the UN and the Dutch state.
The victims lawyers' earlier cited a figure of $4bn as a starting point for compensation negotiations.
But Bert Jan Houtzagers, representing the Dutch state, told the three-judge tribunal that a ruling for the victims would have broad implications.
"It is not true that the United Nations believes it is over and above the law, but the question is whether a Dutch court is competent to hear a case against it," he said.
"Because if a Dutch court does, any court in any country could do so and that would thwart the viability of the United Nations."
But Hagedorn said if the Dutch court refused to hear the suit, it would leave the victims with no venue for their claims, in contravention of international treaties on genocide.
Marco Gerritsen, another lawyer for the victims, said the UN and Netherlands "should not hide behind each other or each point the finger at the other" to avoid claims.
The case is one of several seeking to determine whether the Netherlands and the UN can be held liable for failing to carry out a promise of protection for civilians in the UN enclave.
The court said it will take several months to rule on UN immunity and did not set a date for a decision.
An independent report by the Netherlands Institute for War Documentation in 2002 placed partial blame for the massacre with the Dutch government for sending its ill-prepared troops on an impossible mission.
It faulted the UN for designating the area a "safe haven" for Bosnian war refugees, but not defining what that meant.
The report led the Dutch government to resign, but the state denied liability for the murders, saying that rested with the Serb forces.
The UN war crimes tribunal set up to prosecute war crimes committed during the break-up of the former Yugoslavia is still seeking the two prime criminal suspects in the Srebrenica massacre: General Ratko Mladic, who commanded Serb forces in Bosnia; and Radovan Karadzic, the political leader of Bosnian Serbs.
A petition by Bosnia seeking war reparations from Serbia was rejected by the International court of justice in the Hague.
Republika Srpska, the Serb-dominated province within Bosnia, paid about $31m for the creation of a memorial and for the reconstruction of the infrastructure in and around Srebrenica.
The Netherlands donates about $23m annually in aid to Bosnia.