Washington has said in the past that Cuban authorities must take responsibility for the safety of United States diplomats on their soil, but the Havana government denies any knowledge of an attack.
The FBI launched an investigation that lasted a year following attacks in Havana, but they were unable to determine what caused the phenomena.
Nauert also said that remaining US government personnel and their families in Guangzhou would also be able to request testing if they "noted concerning symptoms or wanted baseline screening".
The incidents have raised fears the unexplained issues that started in Cuba in 2016 have expanded to other countries. The U.S.is also examining new potential cases from a U.S. consulate in China.
The US government began withdrawing diplomats from its embassy after embassy personnel began to report hearing unusual noises and experiencing a string of similar medical symptoms in late 2016. It called for people to be attentive of symptoms including "dizziness, headaches, tinnitus, fatigue, cognitive issues, visual problems, ear complaints and hearing loss, and difficulty sleeping".
Recall that from China sent several American diplomats and their family members to undergo medical examinations.
Canada in April also ordered families of diplomatic staff in Cuba to return home after mysterious health symptoms were detected in 10 Canadians stationed on the island.
The incidents have raised concerns that a government or agency may be targeting the United States with a new type of sonic weapon.
The China incidents affect one of the most important of the seven US diplomatic outposts in the country.
Cuba on Sunday said it had no explanation for a USA government employee's report of sounds heard in her home two days before she started having health issues, The Hill reports.
Since the incident, other employees from the consulate and their families have been evacuated. The 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.
The statement said Cuba reaffirmed its desire to "cooperate with the USA authorities to clarify the situation".