Supporters of Ejup Ganic protest in the Bosnian capital Sarajevo
Former Bosnian president Ejup Ganic will remain in jail in London while his application for bail is considered.
Mr Ganic, 63, was arrested at Heathrow Airport on Monday at the request of Serbia, where he is wanted on war crimes charges.
But the Bosnian authorities say he should be extradited there instead.
Thousands of Bosnians protested outside the British and Serbian embassies in the Bosnian capital Sarajevo demanding his release.
Mr Ganic, a friend of Baroness Thatcher, had his application for bail postponed at the High Court on Friday.
The judges adjourned a ruling until Thursday to give the Crown Prosecution Service more time to gather material supporting its case that he should be detained pending extradition proceedings.
Serbia has accused Mr Ganic of murder and involvement in war crimes in 1992.
His family and lawyers claim the charges are politically motivated.
In London, Mr Ganic's son, Emir, and his daughter, Emina, said they had not been allowed to see their father for three days after his arrest.
"My father was denied access to the ambassador, to us and to his lawyers, and he was denied phone calls from the prison," he said.
"He had no clue what was going on."
His daughter added: "We continue to be surprised at the ability of Serbia to have my father arrested and held in prison on a provisional arrest warrant that has no merit."
The Bosnian government has told the British ambassador in Sarajevo it is not happy with what it described as the inadequate treatment of Mr Ganic.
The Foreign Office has said his arrest is not a political or diplomatic statement by the UK government, but a case of the judicial authorities following their legal obligations.
Mr Ganic was arrested while visiting the UK for a degree ceremony at the University of Buckingham, which is partnered with the the University of Sarajevo school of science and technology, where he is president.
He has travelled freely to Britain several times in recent years, but was arrested under a provisional extradition warrant as he tried to leave the country on Monday.
The provisional extradition warrant relates to an attack on Yugoslav forces in Sarajevo at the beginning of the 1992-1995 Bosnian war.
Serbia claims more than 40 soldiers were killed in the so-called Dobrovoljacka Street attack, after Bosnia had declared independence from the Serb-led former Yugoslavia.
The soldiers were allegedly withdrawing from Sarajevo in a convoy at the time.
Mr Ganic is one of 19 people for whom arrest warrants were issued in November and sent to Interpol.
Serbia has 45 days, from 3 March, to provide full papers to the court supporting its extradition request.
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