Authorities promised to reopen the span as soon as the refugees started moving toward camps.
The refugees fled ahead of Monday's deadline for French troops to withdraw from a safe area they established in Rwanda in June. The mostly Hutu refugees do not trust UN peacekeepers replacing the French to protect them.
Hutu refugees fear Tutsi revenge for massacres in Rwanda's 14-week-old civil war. Up to 500,000 people have been slaughtered in the conflict, most of them minority Tutsis killed by Hutu soldiers and militiamen.
Several thousand refugees waited calmly for the bridge across the Rusizi River to reopen. Thousands more advanced upon it in a steady stream from another bridge 10 kilometers to the north, which Zaire closed Saturday.
The exodus has led to fears of a repeat of the refugee crisis that blindsided Goma, Zaire, 100 kilometers to the north. There nearly 1 million Rwandans poured across the border in three days last month, and some 43,000 of them died of malnutrition, cholera, dysentery and other illnesses.
The other bridge, closer to Bukavu, was shut because authorities were afraid the flow of refugees was out of control and could heighten the risk of deadly epidemics in Bukavu's filthy, overcrowded camps. At least 100,000 refugees are housed in those camps, and cases of cholera and dysentery have already been found.
On Sunday, a pushing, shoving mob at the border bridge overwhelmed UN peacekeepers from Ethiopia guarding the Rwandan side of the span. Zairean soldiers beat the refugees back with canes and sticks.
In response to the chaos and mounting UN pressure, Zaire reopened a second bridge over the Rusizi River. That southern bridge had been closed for weeks and remained unused by refugees seeking to escape Rwanda.
About 20,000 frightened men, women and children were moving toward the bridge, a spokesman for the UN High Commissioner for Refugees said.
The spokesman, Ray Wilkinson, estimated that at least 45,000 would cross the bridge in the next few days, including thousands still en route from villages and towns in southwestern Rwanda.
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