People who have traveled to cities or counties where just a single COVID-19 case has been reported in the past two weeks are barred entry.
That leaves open the possibility of patients with underlying conditions aggravated by the virus being excluded from the toll if they die of those conditions after meeting the official criteria for COVID recovery.
China's health commission told AFP its toll counts virus-infected people who die without first recovering from COVID.
Countries have used different methodologies to identify and count coronavirus deaths, however, making comparisons difficult.
The service area covers about 512,799 residents in Bell, Coryell, Hamilton, Lampasas, Milam, and Mills counties.
Texas, Florida and New York followed, with death tolls ranging from about 68,000 to 88,000.
Doubts have been raised over the efficacy of China's homegrown vaccines, and Beijing has not imported any foreign-made jabs.
The populous eastern district of Chaoyang said it would expand Covid testing, adding that it had indefinitely banned extracurricular in-person classes or sports activities.
China's biggest city only announced its first fatalities from the outbreak on April 18, despite reporting thousands of cases each day in recent weeks.
Description: The world's second-largest economy has been struggling to stamp out its worst outbreak in two years with a playbook of harsh lockdowns and mass testing as it sticks to a strict zero-COVID policy, taking a heavy toll on businesses and public morale.