One path would be for the United States to suggest that the two countries conduct a joint investigation, they added.

In a statement released on Wednesday night in Washington, the State Department’s spokeswoman, Heather Nauert, said: “As a result of the screening process so far, the department has sent a number of individuals for further evaluation and a comprehensive assessment of their symptoms and findings in the United States.”

The statement did not disclose how many complained of the illness associated with the mysterious sounds and sensations. A State Department statement this week listed the symptoms as “dizziness, headaches, tinnitus, fatigue, cognitive issues, visual problems, ear complaints and hearing loss, and difficulty sleeping.”

According to experts who studied the previous cases in Cuba, those afflicted so far in Cuba and Guangzhou — suffered injuries consistent with a concussion without ever having received a blow to the head.

One official said that “a sizable number” of people working in Guangzhou had requested examinations, which are being carried out in the consulate’s medical facilities. The officials cautioned that not everyone who experienced the sonic effects or showed symptoms would necessarily show signs of injuries.

The consulate is the largest by far in China, and is a major site for the issuing of visas for travel to the United States. Many of the American diplomats are in their first or second postings overseas, making the mysterious nature of the illnesses particularly unsettling.

In addition to the State Department’s medical team, which arrived on May 31, specialists from the Centers for Disease Control and Prevention also arrived in China this week to join in the investigation in Guangzhou.