Bruno Rodriguez insisted there is no evidence tying Cuba to mysterious attacks on diplomats in Havana.
The move is in response to the string of unexplained attacks harming US diplomats in Havana.
US visitors were not hurt by the unexplained incidents harming diplomats, travel groups argue.
Tillerson met with Cuban officials on Tuesday to discuss unexplained incidents harming US diplomats in Havana.
Cuba denied involvement in alleged attacks that left Americans with symptoms such as hearing loss and concussions.
Criticism of Cuba was included in a speech that mostly focused on North Korea, Venezuela and Iran.