The Agriculture Department is now trying to trace any animals born on the ranch in the same year or in the years before or after, as well as any offspring of the cow born in the last two years. All will be tested for the disease, which will mean killing them because parts of the brain must be scooped out to do the tests.

Dr. Clifford would not identify the ranch, calling that "privileged information." Nor would he name the pet food plant, explaining that the department relied on the voluntary cooperation of such plants for brain samples. They specialize in turning diseased, dying and dead animals into pet food or into dried meal for poultry and pigs, as well as into tallow, gelatin and other products.

It is too early to tell what effect the announcement will have on beef sales. On Saturday, after it became clear that the United States had a second case of mad cow disease, or bovine spongiform encephalopathy, and that it did not originate in Canada as the first had, Taiwan reimposed a ban on American beef it had lifted two months ago.

But domestic beef sales and futures prices have remained relatively steady.

Asked whether any other states might ban imports of Texas cattle, Dr. Clifford said he hoped not. "It wouldn't make sense with the safeguards we have in place," he said.

Gov. Rick Perry of Texas issued a statement urging citizens to remain calm and be reassured that they could trust the state's beef.