The Cuban government denied involvement in the attacks and the State Department sent more than 60 percent of Americans working at the US embassy there home.
However, he indicated that the precise nature of the health problems has not been determined nor it is known if there is a common cause for the cases registered in the Caribbean island or in China.
The medical screenings in China are continuing, Nauert said.
The statement said Cuba was informed of one case in late May where "a functionary of the (U.S.) embassy on the 27th of the same month had reported health symptoms as a result of "undefined sounds" in her residence".
But President Donald Trump and other USA officials have accused Cuba of having targeted US personnel with some kind of "acoustic sonic weapon" for unknown reasons, an allegation the Cuban government has forcefully denied.
Those affected have suffered a range of symptoms including hearing loss, dizziness, fatigue, cognitive issues and sleep loss.
Secretary of State Mike Pompeo last week announced that the U.S.in May established a Health Incidents Response Task Force to look into "unexplained health incidents" affecting Americans in Cuba and China. The U.S.is also examining new potential cases from a U.S. consulate in China. The Canadian government followed suit in April and directed the families of diplomatic staff in Cuba to return home. Canada said the 10 continued to show unexplained brain symptoms and that "medical information raised concerns for a new type of a possible acquired brain injury".
Secretary of State Mike Pompeo announced the formation of a task force in response to "unexplained health incidents" affecting USA diplomats and their family members.
The China incidents affect one of the most important of the seven US diplomatic outposts in the country.
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.
"We are continuing to work with the Department of State to evaluate and treat personnel who have reported audible phenomena experiences", according to a health system statement.