The Serbian government has ruled out any possibility of a state funeral or ceremony, but Kostunica's comment appears to pave the way for a private ceremony and burial.
Kostunica's announcement follows a decision by a Belgrade court today to suspend the arrest warrant for Milosevic's widow, a move that could clear the way for her to attend her husband's funeral in Serbia from Russia.
Markovic is facing abuse-of-power charges in Serbia.
But news agencies report the court also ordered Mirjana Markovic to surrender her passport on arrival and appear at a hearing.
Meanwhile, Milosevic's son, Marko, has flown to the Netherlands to claim his father's body. Marko Milosevic had raised the possibility that his father's funeral could be held in Moscow because, he said, the Belgrade authorities did not want to hold it in Serbia.
Milosevic died on March 11 in the detention center of the UN war crimes tribunal for the Former Yugoslavia, where he was facing charges of genocide, war crimes, and crimes against humanity.
(compiled from agency reports)
In Poor Health
Slobodan Milosevic in an undated file photo (CTK)
HEART TROUBLES, HIGH BLOOD PRESSURE: Almost since the beginning of his trial in The Hague in February 2002, Slobodan Milosevic has been complaining of ill health. His trial has been repeatedly delayed as he sought medical treatment. As recently as February 24, the court declined Milosevic's request to travel to Russia for treatment for heart problems and elevated blood pressure, despite pledges from Moscow that Milosevic would be returned to The Hague to continue his trial on 66 counts of war crimes and crimes against humanity.
"[My health is] getting worse because of the decision that gives me no chance or adequate time to prepare my defense, and that is pretty clear," Milosevic told the court on July 5, 2004. " Because of that, I think that you have an obligation to give me adequate time."
"[The judges] have been very clear that there is no evidence to suggest that Mr. Milosevic is not fit enough to stand trial," court spokesman Jim Landale told journalists the next day. "They have decided that the time has possibly come for them to assign what is called a 'standby counsel.' That is a lawyer who would work alongside Mr. Milosevic and, were Mr. Milosevic to become ill again, be able to step in and represent his interests in court."
Of related interest:
THE COMPLETE PICTURE: An archive of RFE/RL's coverage of the trial of former Yugoslav President Slobodan Milosevic.
Of related interest: