In October, the U.S. State Department ordered non-essential embassy workers and their families to evacuate Havana out of concern the mysterious illness was the result of a targeted sonic attack.
Washington has said in the past that Cuban authorities must take responsibility for the safety of U.S. diplomats on their soil, but the Havana government denies any knowledge of an attack.
China earlier said it had looked into the case announced last month but came up with no clues about the cause of the symptoms.
Nauert also said that remaining USA government personnel and their families in Guangzhou would also be able to request testing if they "noted concerning symptoms or wanted baseline screening".
The case revived fears that a USA rival has developed some kind of acoustic or microwave device after similar symptoms were reported among American diplomats and their families in Cuba in 2016.
Symptoms suffered by the diplomats have included hearing loss, tinnitus, vertigo, headaches and fatigue, a pattern consistent with "mild traumatic brain injury", State Department officials have said.
A security person walks outside the USA consulate building in Guangzhou in south China's Guangdong province, Thursday, June 7.
Earlier this week the USA removed diplomats from the southern Chinese city of Guangzhou, after they reported symptoms and unusual sounds.
In April, Canada said it would remove families of diplomats posted at its embassy in Cuba as information from medical specialists has raised concerns of a new type of brain injury.
The Cuban response comes after the USA withdrew two more people from the U.S. embassy in Havana, Cuba, due to health concerns, according to a senior State Department official. There are about 170 US diplomats or employees and their families in Guangzhou.
The New York Times identified the latest American employee evacuated as Mark A. Lenzi, a security engineering officer at the consulate who left Wednesday night with his wife and two children. The Guangzhou consulate opened months after the establishment of diplomatic relations between Beijing and Washington in 1979 and moved to its new purpose-built facility in 2013. According to the statement, authorities could not find the source of the sound.