The United States and Iran are at loggerheads over Tehran's nuclear program and Washington has blamed Iranian forces for attacks on oil tankers in the Gulf region, a charge Tehran denies.
The two nations came close to conflict last month when Iran shot down a U.S. drone, prompting Washington to order retaliatory air strikes that were called off at the last minute.
Zarif will attend a meeting of the U.N. Economic and Social Council (ECOSOC) in New York and would then travel to Venezuela, Bolivia and Nicaragua, IRNA reported.
U.S. Treasury Secretary Steven Mnuchin said in June that Washington would impose sanctions on top Iranian officials, including Zarif, a step that could have impeded any diplomatic efforts to resolve their disagreements.
But two sources familiar with the matter told Reuters on Thursday the United States had decided not to impose sanctions on Zarif for now, in a sign that Washington might be holding a door open for diplomacy.
President Donald Trump withdrew the United States last year from a 2015 accord between Iran and world powers that had aimed to curb Tehran's nuclear program.
Washington has ratcheted up sanctions on Iran since then, driving Iranian oil exports sharply lower.