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United Nations officials say it is the biggest "ethnic cleansing" operation since World War II.
Some 40,000 women, children and elderly people have been ordered to leave the compound at Potocari where they had been under the protection of Dutch peacekeepers.
The Dutch soldiers - part of the UN peacekeeping force - appear to have been powerless to defend Srebrenica against the Serbs who seized control of the town on 11 July.
Reports say all Muslim men over 16 were rounded up as they attempted to flee the advancing Serbs - but these have not yet been confirmed.
The Bosnian Serbs have refused access to journalists and international organisations.
There are many tales of atrocities - rape, massacres and psychological torture - circulating among the refugees now arriving in the northern Bosnian town of Tuzla.
The biggest fear is for the men who have been left behind. Many wives and families fear they will never see them again.
One woman told relief workers she had seen the Serbs slit her husband's throat and that she had seen at least eight other bodies.
The Bosnian Prime Minister, Haris Siladjdzic, has blamed the Bosnian Serbs for the atrocities.
"Massive massacres were committed by Serbian terrorists upon the civilians of Srebrenica," he said.
"There are hundreds of witnesses that arrived yesterday to Tuzla, speaking of horrendous crimes there; hundreds of bodies, naked, stabbed and killed by Serb terrorists."
The refugees are huddled together in flimsy shelters in a temporary UN camp.
Anne-Marie Huby of Medecins Sans Frontieres said: "These people are already survivors of earlier waves of ethnic cleansing in 1992 and 1993.
"They really thought, when they saw the Serbs come in this time, that it was their last hour. Our aid workers say people are absolutely convinced they will not see their men again."
The makeshift camp has virtually no toilets and aid workers are warning that diarrhoea could become endemic within days.
Thousands spent last night sleeping rough and have no daytime shelter from the strong winds and blistering sun, leading to fears of mass dehydration and heat exhaustion.
The United Nations has begun busing refugees out of the reception camp to other sites so they can be better cared for.
The Bosnian Serbs now appear to have their sights set on Zepa and Gorazde, two other UN-designated "safe areas". If they succeed in taking them, then there will be virtually no Muslims left in the eastern half of Bosnia-Herzegovina.
More details of the atrocities committed in the capture of Srebrenica emerged over the following weeks.
On 12 August 1995 the UN announced an investigation into reports up to 2,700 Muslim men had been shot dead with machine-guns and buried in mass graves. US aerial photographs appeared to show evidence of mass graves close to Srebrenica.
Refugee accounts claimed General Ratko Mladic, the Bosnian Serb commander, addressed the Muslim captives and warned that 1,000 refugees would be killed for every Serb who died.
General Mladic was later indicted by the War Crimes Tribunal for genocide but is still at large. One senior Bosnian Serb, General Radislav Krstic, has been jailed for genocide for his part in the Srebrenica tragedy.
It is now thought that between 7,000 and 8,000 Muslim men were killed by Serb soldiers following the fall of Srebrenica.
The massacre is regarded as the worst atrocity in Europe since World War II.
There have been a number of investigations into the massacre. In 2002 the entire Dutch government resigned after an inquiry blamed officials for giving the poorly-armed troops an impossible task to defend the enclave.
Initial findings of a commission involving the Bosnian Serbs admitted for the first time in June 2004 that Serbs had taken part in the killings.
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