Zagreb says Serbia's crimes included murder, torture and the destruction of property.
In its suit, Croatia said: "All of these actions were specifically and purposefully undertaken with the intent to destroy, in whole or in part, national, ethnic, or racial group."
Presenting their opening arguments, Serbia's lawyers said the court had no jurisdiction in the case because the country was not a member of the United Nations at the time the suit was filed.
As a result, Serbia says it not subject to the genocide convention and it also denies that genocide took place.
Tibor Varady, Belgrade's chief legal representative, said: "This is a case in which there was no genocide."
Varady said that while he acknowledged "the true suffering of Croats" there had been victims on both sides.
"The conflict in the former Yugoslavia cannot be reduced... to a simple scale of one villain and one victim. Misdeeds on one side spurred misdeeds on the other side.
"It is our conviction that a scrutiny of events in Croatia in the early 1990s is not the task of this court," he said.
Varady said that Serbia's relations with Croatia had reached a state of "normalcy" and that a prerequisite for this had been an apology to Croatia by Serbia and the ongoing punishment of war crime perpetrators.
Croatia's opening arguments will begin on Tuesday in public hearings scheduled to last until Friday.
Two years ago, the court heard a similar case brought by Bosnia, which relied heavily on the argument that the massacre of 8,000 Muslims by Bosnian Serbs in the UN safe zone of Srebrenica amounted to genocide by Serbia.
The court cleared Serbia last year, saying the massacre was genocide but Serbia was guilty only of failing to prevent it and punish perpetrators.
Croatia broke away from Yugoslavia in a process that began in 1991, and tried to quell the Serb minority there.
As a result, the Serb minority, later backed by the Yugoslav army, tried to conquer as much of the country as it could to redraw its borders.
Bosnian Serbs, backed by Serbia, swept swaths of land clean of non-Serbs, culminating in the Srebrenica massacre.
Three-quarters of those killed during the war were Muslims and Croats.
The hearings at the court, set up after World War Two to mediate in disputes between states, are due to run until May 30.
The core complaint cannot be heard before a decision has been made on Belgrade's objection on jursidiction, which could take six to eight months.