NAIROBI, Kenya, May 20— As many as 10,000 bodies from Rwanda's massacres have washed down the Kagera River into Lake Victoria in Uganda in the last few weeks, creating an acute health hazard, a senior Ugandan official says.

Cloaking the countryside with the stench of death, the bodies -- as many as 100 an hour -- are being washed ashore in the Rakai district of southern Uganda or onto islands in Lake Victoria and have been seen as far north as Entebbe.

A clean-up operation by the Ugandan Government and international relief agencies has been hampered by the remoteness of the area, heavy rains and the difficulty of fighting off the wild animals and dogs feeding on the bodies. Worried about epidemics of cholera and other diseases, the Health Ministry of Uganda is telling villagers to boil drinking water and to cook all fish thoroughly.

"It's basically an appalling sight," said Keith Sherper, the director of the United States Agency for International Development in Kampala, who is assisting the Ugandan Government in the clean-up.

The Kagera River flows through southern Rwanda, mostly through Government- and militia-controlled territory, and bodies have been carried by the current for weeks. Relief officials say the killers must have dumped the bodies into the river by the truckload. Many are mutilated.

"I've never seen hatred like this in my life," said Manuel Pinto, a member of the Ugandan Parliament from the Rakai district and the head of the clean-up operation who gave the estimate of up to 10,000 bodies. "There are so many of them. Children are skewered on sticks. I saw a woman cut open from the tail bone. They have removed breasts and male genital organs."

The massacres in Rwanda began on April 6 when its President, Juvenal Habyarimana, was killed in a suspicious plane explosion. Most of the killings have been done by the majority Hutu military and militia and have been directed against the minority Tutsi tribe in what human rights officials say is an "ethnic cleansing" of the Tutsis. Battle deaths in fighting between the military and the Tutsi rebels have been relatively few in comparison.

Reliable estimates of the death toll are hard to find, but some range up to and beyond 200,000.

The Kagera River empties into Lake Victoria in the Rakai district near the fishing village of Kasensero, once an important trading center but now decimated by AIDS and with about 1,000 inhabitants. It was in Kasensero that the first cases of AIDS were reported in the 1980's.

The clean-up operation in Uganda began on April 25 but was at first limited to a local effort. Western donors have now pledged more than $150,000. World Vision International and the Lutheran World Federation are the two main relief agencies, but in a broad show of support, Ugandan volunteers are providing time, money, trucks, fuel and excavators for mass graves. The Ugandan Government is trucking in drinking water. Working Round the Clock

Workers are trying to remove bodies before they reach the lake, and crews work round the clock, Mr. Pinto said. They use motorized canoes and must somehow trap the bodies, pull them to shore, wrap them and load them onto trucks.

Many bodies have already washed ashore and are rotting. This attracts wild animals and dogs and fills the area with a gagging stench. On one island, as many as 700 bodies had washed ashore, Mr. Pinto said.

At first villagers dug shallow graves, but heavy rains have washed away the sandy earth and exposed the bodies. Mr. Pinto said the clean-up force has assigned people to shoot scavenging dogs. The rains have also made dirt roads impassable, and the bodies have to be ferried with the canoes.

There is the danger of pollution as well. Lake Victoria, the second largest body of fresh water in the world, borders Uganda, Tanzania and Kenya and is also the source of the Nile. The fishing of Nile perch is the backbone of local economies. Health experts believe that the perch, who like to eat live prey, will not feed on the bodies, but the experts have advised the local inhabitants to cook the fish thoroughly.

Photo: Bodies lying by Rusumo Falls on the Kagera River, at the Rwanda-Tanzania border, on May 2. (Jean-Marc Bouju/Associated Press)(pg. 1) Map of Tanzania showing location of Kagana River. (pg. 6)