The plaintiffs comprise a group called "Mothers of Srebrenica", who represent some 6,000 survivors, and 10 individual widows who lost their husbands in the assault.
They are seeking a trial for the UN and the Dutch state for the peacekeeping troops' alleged failure to protect the enclave.
But the Dutch state brought a counter-application, arguing the court had no jurisdiction to hear a case against the UN which, it argued, enjoyed immunity.