Fausto Pocar, the tribunal president, said at a Sunday news conference that an autopsy was ordered after the Dutch forensic team failed to learn the cause of death.
Carla del Ponte, the chief UN war crimes prosecutor, told the same news conference that "it is a great pity for justice that the [Milosevic] trial will not be completed and no verdict will be rendered".
His death "deprives victims of the justice they need and deserve", del Ponte said, and made "more urgent than ever" the arrest and extradition of Radovan Karadzic, the wartime Bosnian Serb leader, and his top military commander, Ratko Mladic, for crimes committed during the Balkan wars in the 1990s.
Both men are charged with genocide.
Del Ponte also said she could not rule out that Milosevic might have committed suicide.
"Of course it (suicide) could be possible," she said.
She added that initial results of the autopsy on Milosevic were expected later on Sunday or on Monday, although toxicology test results could take longer.
The authorities hope that the autopsy will put to rest claims that Milosevic was murdered.
Carla del Ponte (R): Milosevic
death a great pity for justice
Milosevic was found dead on Saturday in the detention centre of the International Criminal Tribunal for the Former Yugoslavia (ICTY) where he was on trial for war crimes, crimes against humanity and genocide for his roles in the 1990s Balkan wars that killed more than 200,000 people.
His body was taken to the institute in The Hague for the autopsy which will be attended by Serbian government medical experts.
Milosevic's family in Moscow and political allies in Belgrade have raised suspicions about his death, blaming the UN court. A legal aide said Milosevic feared he was being poisoned while in custody.
Last month, the judges denied a request from Milosevic, 64, who suffered from high blood pressure and heart problems, to undergo medical treatment in Moscow, saying he could be treated by his Russian doctors in The Hague.
Milosevic's brother, Borislav, said the tribunal's judges bore "full responsibility" for his death. Serbian newspapers accused the tribunal of murder.
Zdenko Tomanovic, a legal adviser to Milosevic, said the former Yugoslav president claimed to have been the target of an attempted poisoning.
The ICTY said a toxicological examination of the body would also be carried out.
An ICTY spokeswoman said there was no sign that he committed suicide, and added: "We cannot say that he died of natural causes. We are waiting for the report."
Christian Chartier, the tribunal spokesman, said: "The tribunal has nothing to be blamed for."
Milan Babic committed suicide
after admitting his guilt
His death was announced six days after the suicide in the same prison of his former ally, 50-year-old Croatian Serb ex-leader Milan Babic, who pleaded guilty to crimes against humanity during the 1991-95 war in Croatia.
Milosevic had been on trial since February 2002 on more than 60 counts of war crimes and crimes against humanity. He also faced genocide charges related to the 1992-95 war in Bosnia, where Serb military strategies devised to depopulate non-Serb areas became known as "ethnic cleansing".
On the streets of Belgrade, Serbs reacted with a mixture of shock, anger and deep suspicion. Some called him a "bastard" for whom death was too kind, while others wept at the loss of a national "martyr".
Serbia's media focused on the UN court's perceived culpability.
"The Hague killed Milosevic," said the front pages of both Press and Glas Javnosti, against black backgrounds bearing large pictures of Milosevic.
"Murdered," said Kurir, another of the Balkan state's dailies, basing its story on an interview with a Serbian doctor who had examined Milosevic in November.
Some see Milosevic as a 'martyr'
while others call him a 'bastard'
Europe reacted with hope that his death might lead to reconciliation in the region, still divided by nationalist tendencies and the legacy of the Milosevic years.
Javier Solana, the European Union foreign policy chief, said: "I hope very much this event, the death of Milosevic, will help Serbia to look definitely to the future."
Solana is in Salzburg for EU talks with Balkans policymakers.
But there were also fears that Milosevic's death could boost nationalist forces who remain powerful in Serbia and the Serb-run part of Bosnia.
His funeral, if held in Serbia, could be a rallying point for nationalist hardliners who control the largest party in the Serbian parliament.
Milosevic's brother has called for Milosevic to be buried in Belgrade, but said no decision had been taken yet.
Borislav Milosevic said: "It has not been decided. His family - his wife and son - are taking the decision."