Nauert said Washington had informed Havana of the latest incident on May 29, before it was formally medically confirmed, and reminded Cuba of its responsibility to protect diplomats on its soil.
Another US diplomat has reportedly been evacuated from Havana, but the results of his or her tests have not yet been released.
The apparent victims of the mystery ailment have suffered symptoms consistent with mild brain trauma -- including, in some cases, disorientation and hearing loss.
Some American officials in both China and Cuba reported hearing an unidentified noise before falling ill, and initial reports suggested they may have been hit by a secret sonic weapon.
But US intelligence and medical experts have been investigating for more than a year and seem no closer to identifying the cause.
After holding Cuba responsible for either carrying out the attacks or failing to protect its officials, the US recalled more than half of its staff and expelled 15 Cuban diplomats from Washington.
This marked a major diplomatic crisis following the countries' cautious revival of ties in 2015, but Cuba has firmly denied any role in or knowledge of the incident.
On June 10, the Cuban foreign ministry said: "We can confirm that we have no credible hypothesis or scientific explanation that justifies the retaliatory US measures.
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