A Medecins Sans Frontieres team counted 25,000 people reaching the frontier town of Cyangugu on Monday, spokeswoman Samantha Bolton said.
"MSF has the impression there is not much we can do to stop the movement," said Bolton, signalling the growing despair of aid agencies already struggling to cope with about 2.7 million Rwandan refugees outside the devastated nation's borders.
"We have to be there to prepare for the influx and as yet there are no sites prepared in Cyangugu."
Bolton said between 2,000 and 5,000 people were crossing the frontier into the Zairean town of Bukavu each day but most were jamming up against the border on the Rwandan side.
United Nations Rwanda Emergency Organization spokeswoman Sybilla Wilkes said an exodus to Bukavu threatened a crisis unmatched even by the apocalyptic camps of Goma.
"Bukavu does not have the infrastructure to support a large influx of refugees. The results there could be more horrific than Goma," Wilkes told reporters.
Wilkes said the best solution was to establish camps inside Rwanda, just south of Cyangugu, where the refugees could be managed more easily -- if they could be persuaded to stay.
Hutus started moving from deeper inside the safe haven towards Zaire last week, driven by a fear that the pull-out of French troops from Operation Turquoise by next Monday will signal an invasion of mainly Tutsi guerrillas who have taken the rest of Rwanda.
The common rumor is that the Rwandan Patriotic Front is butchering Hutus. The UN is investigating reports of abuses by RPF soldiers but says there is no evidence of a pattern.
An ill-equipped and understaffed UN Assistance Mission in Rwanda is racing to deploy peacekeepers in the place of the French forces who arrived in June.
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