What authority do FBI special agents have to make arrests in the United States, its territories, or on foreign soil?

In the U.S. and its territories, FBI special agents may make arrests for any federal offense committed in their presence or when they have reasonable grounds to believe that the person to be arrested has committed, or is committing, a felony violation of U.S. laws. On foreign soil, FBI special agents generally do not have authority to make arrests except in certain cases where, with the consent of the host country, Congress has granted the FBI extraterritorial jurisdiction.