BUKAVU, ZAIRE, AUG. 19 -- As thousands of Rwandan Hutus continued to flee their country in advance of France's military pullout Sunday, the government of Zaire threatened to close the border with Rwanda to prevent a repeat of the catastrophic human exodus that overwhelmed the tiny Zairian town of Goma last month.

Zairian authorities informed U.N. officials this week of their intention to close the border "if the situation gets out of hand." An official with the office of the U.N. High Commissioner for Refugees (UNHCR) said he expected the border to be shut by noon Sunday.

News of the possible border closing -- and the new Tutsi-dominated Rwandan government's pledge to send troops into the French-protected zone -- appears to have sparked the largest single day's exodus into Bukavu. U.N. officials said refugees were crossing into Bukavu today at a rate of about 30 per minute, for a total of 15,000 to 20,000 new arrivals. About 10,000 Rwandans are estimated to have crossed into Zaire on Thursday.

"If they close the border, people are going to be desperately trying to cross in another way," said Jerry van Mourik, the UNHCR representative in the Rwandan town of Cyangugu, near the border. He predicted that many refugees would try to swim across the Rusizi River to Zaire.

Van Mourik said about 100 heavily armed Zairian troops were already seen approaching the border.

The French government, ignoring appeals that its humanitarian mission continue in Rwanda, said its troops would withdraw completely by midnight Sunday. President Francois Mitterrand and Prime Minister Edouard Balladur issued a joint statement declaring the end of the French mission -- Operation Turquoise -- undertaken at the end of June to protect refugees, mainly Hutus, who had fled to southwestern Rwanda.

"France has fulfilled its duty. ... It is now up to the Rwandan authorities and the international community to assume, as of today, all of their responsibilities," the statement said.

Rwanda's Hutus say they fear retribution by the Rwandan Patriotic Front, a Tutsi-led rebel group that won a renewed civil war after three months of fighting against Rwanda's hard-line Hutu government. The fighting, along with tribal massacres largely carried out by Hutu militias, killed an estimated half-million people, mostly Tutsis and moderate Hutus.

A U.N. force is preparing to take the place of the French troops, but the Hutus say they have no confidence that the U.N. peacekeepers, mostly from Ghana, Ethiopia and Chad, can protect them from the Patriotic Front.

About a million people are believed to be in the French-protected zone. If many of them decide to leave as the French depart, relief workers fear the scene could mirror that of Goma, at the northern end of Lake Kivu, when more than a million refugees fled to Zaire and tens of thousands succumbed to cholera, dysentery and other illnesses.

There are already an estimated 50,000 Rwandan refugees in the Bukavu area, with about 80,000 believed to be in the town center and surrounding neighborhoods. Today's new arrivals began pitching tents, chopping down trees, and grazing their cattle on grassy median strips down the main road.

The United Nations has been trying to move refugees out of the town and into 14 designated camp sites. But many of the camps are far from town and their capacity is small. In addition, the United Nations has said it has limited transportation for a large-scale move.

U.N. officials have said it is essential to transfer the refugees out of the city because of the growing threat of disease and also because of what UNHCR spokesman Kris Janowski called "the mounting tension" in Bukavu.

Several violent incidents have been reported between Zairians and refugees; in some cases refugees attacked aid workers whom they accuse of not doing enough to assist them.

Relief officials estimate tens of thousands of additional refugees are heading west through the Nyungwe forest that separates Gikongoro, at the eastern edge of the protection zone, from Cyangugu, making the treacherous 75-mile walk over hillside roads through rain and cold.

An official of the International Committee of the Red Cross estimated that there were about 40,000 people on the main road heading west.

UNHCR's Van Mourik said he believed about 60,000 people were on the road stretching from the western edge of the forest, at the town of Gisakura, to Cyangugu.

In Gikongoro, some of the large refugee camps appeared to be emptying, as tens of thousands of people packed their belongings to begin the five-day trek to Zaire. At the Cyanika camp, which held some 80,000 displaced people two weeks ago, only about 18,000 are left, according to Irish nurse Siobhan Corkery.

"The weak and the poor are staying because they can't afford to go," she said.