Dr. Bresee said that he empathized with evacuees who want definitive answers about whether they are healthy.

“They’re concerned, they’re nervous, and they want to be assured of their safety,” he said, adding that the cost of testing was not a factor in the decision not to test everyone. “We don’t think testing would be helpful, and if we did, we would test them.”

About 1,000 Americans are believed to live in Wuhan, where the outbreak began. As the number of confirmed cases soared and commercial carriers suspended flights out of the city, the United States began chartering planes to bring home citizens who were stranded there.

On the San Diego base, where evacuees have been waiting since last week, not everyone was calling for more testing. John McGory, who is among the group, said some people did not support the petition. Some in the group said fears had been blown out of proportion and that the C.D.C.’s approach seemed reasonable.

The C.D.C. on Thursday announced the latest confirmed coronavirus case in the United States as having been identified among the evacuees at Joint Base San Antonio-Lackland. The person had been under quarantine on the base until symptoms emerged. The person was taken to a hospital and was stable with mild symptoms, the C.D.C. said. In announcing the new case, the C.D.C. said there would likely be more confirmed cases in the coming days.

At the San Diego base, Marine Corps Air Station Miramar, Mr. Wilson and others said that people had to leave their rooms to get breakfast, lunch and dinner from a small room, which is also where their temperatures were taken. People rummaged through boxes of fruit and snacks with their bare hands, he said, and they stood shoulder to shoulder in line waiting to check their temperatures despite being told to stay six feet away from one another.

After the petition was circulated, health officials agreed as of Thursday to deliver meals and take temperatures at the room doors of evacuees who preferred it that way.