Local authorities told CNN that Americans are being held on conspiracy charges, but they are not formally charged by Haitian authorities.
Three others have been arrested, two foreign nationals and one Haitian, Edmond said.
The identity of the persons taken into custody was not readily available.
Moise's administration has been set on fire for rising inflation and corruption allegations.
In a television address on Saturday night, Haitian Prime Minister Jean-Henry Céant called on the calm and promised to uncover corruption – which for many is the basis of the country's problems.
Referring to the government's own auditor's report on how revenues from Venezuelan subsidized oil were knocked out, he said: "Corruption is one of the biggest problems. We must fight corruption."
On Thursday, the US State Department issued a Level 4 "Do Not Travel" Travel Advisor for Haiti reference to "crime and civil unrest" and "widespread, violent and unpredictable demonstrations in Port-au-Prince and elsewhere in Haiti."
The State Department ordered all "non-emergency US staff and their families" to leave Haiti and said the country had "limited ability to provide relief to US nationals in Haiti." "Protests, tire burning, and blockage of roads are frequent and unpredictable," the advisory said.
"Violent crime, such as armed robbery, is common. The local police may lack the resources to respond effectively to serious criminal events and preparedness, including ambulance service, is limited or non-existent."
CNN's Miguel Marquez reported from Port-au-Prince and Christina Maxouris wrote from Atlanta. Ray Sanchez, Hira Humayun and Radina Gigova have contributed to this report.