Ex-Bosnian Serb army chief Ratko Mladic has been declared fit to be extradited from Serbia to face trial in The Hague.
Court spokeswoman Maja Kovacevic said the transfer conditions had been met.
Gen Mladic's legal team say he is in poor health and that they will appeal on Monday, but Serbian President Boris Tadic insisted he would be transferred to The Hague.
Gen Mladic, arrested on Thursday after 16 years on the run, faces genocide charges over the 1992-95 Bosnian war.
He was indicted in 1995 over the killings about 7,500 Bosnian Muslim men and boys that July at Srebrenica - the worst single atrocity in Europe since World War II - and other crimes.
Mr Tadic told the BBC the authorities' investigations would now extend to anyone who protected the former army chief, enabling him to avoid capture for so long.
They would look at any help given to him by members of the armed forces or police, he added.
Serge Brammertz, chief prosecutor at the UN International Criminal Tribunal to the former Yugoslavia, said he was considering putting Gen Mladic on trial together with former Bosnian Serb political leader Radovan Karadzic.
Mr Karadzic was arrested three years ago and has been on trial since 2009. Any joint appearance would mean lengthy delays in his proceedings, correspondents say, as it could take months before Gen Mladic is ready to go to trial.
Judge Kovacevic told reporters outside the court that Gen Mladic's health was good enough for him to be tried at the tribunal.
"It has been certified that Ratko Mladic is healthy enough to take part in that [extradition], because all medical examinations have been carried out and we got an assessment that he's capable, despite the fact that he suffers from a number of chronic conditions."
He had refused to accept a copy of the tribunal's indictment, she added. After this, the court ruled that the conditions for his transfer had been met and he was given until Monday to appeal.
Defence lawyer Milos Saljic confirmed that an appeal would be submitted on Monday. The judge then has up to three days to consider the appeal, though the BBC's Mark Lowen, in Belgrade, says the matter may be dealt with more quickly.
Gen Mladic's wife Bosiljka and their son Darko turned up at the court to visit him. Mr Saljic later said this was their first meeting with him in 10 years.
Darko told journalists his father was innocent and not in a fit state to be sent to The Hague.
He said the family was asking for an assessment of his health by independent experts, including some from Russia.
Gen Mladic had an electrocardiogram heart test and a brain scan, which revealed two scars from cerebral haemorrhages, Darko Mladic added.
Mrs Mladic only recently said she thought her husband was dead.
Having lived freely in the Serbian capital, Belgrade, Gen Mladic is believed to have gone into hiding after the arrest of former Yugoslav President Slobodan Milosevic in 2001.
Following the detention of Mr Karadzic in 2008, Gen Mladic became the most prominent Bosnian war crimes suspect at large.
The arrest was hailed internationally.
On Thursday, Serbian TV showed footage of the former general wearing a baseball cap and walking slowly as he appeared in court in Belgrade for the first time.
Reports in Serbian media suggested that one of Gen Mladic's arms was paralysed, which was probably the result of a stroke.
Serbia had been under intense international pressure to arrest Gen Mladic and send him to the Hague tribunal.
The government is now keen for a speedy extradition of Gen Mladic, whom Serb nationalists still regard as a hero, our correspondent says.
President Boris Tadic said Gen Mladic's arrest had brought Serbia and the region closer to reconciliation, and opened the doors to European Union membership.
A spokeswoman for families of Srebrenica victims, Hajra Catic, told AFP news agency: "After 16 years of waiting, for us, the victims' families, this is a relief."
Gen Mladic was seized in the province of Vojvodina in the early hours of Thursday, reportedly as he went out into his garden for a pre-dawn walk.
He had two guns with him, but put up no resistance, officials said.
Serbian security sources told AFP news agency that three special units had descended on a house in the village of Lazarevo, about 80km (50 miles) north of Belgrade.
The single-storey house was owned by a relative of Gen Mladic and had been under surveillance for the past two weeks, one of the sources added.
In the latest revelations, police officials told the Associated Press that Gen Mladic had moved to the village two years ago. They also said he admitted his identity immediately in a whisper when found.
AP quoted officials as saying no-one would receive a reward for his arrest, because police were not acting on a tip-off when they arrested him.
Lawyer Milos Saljic told Serbia's B92 news agency that Darko Mladic had visited Lazarevo just a week ago but had no idea his father was there.
Local resident Zora Prodanovic told the BBC: "I'm really surprised. My mother lives four doors down from here and I've never seen him."
"People are shocked, furious, fuming. Our government should stop this bloody business," said another, Momcilo Zivkovic.
"They have arrested our general, who'd defended those who were defenceless; he's now facing false allegations."