The advisory, issed by the FAA on Thursday and circulated late on Friday, said the warning came amidst "heightened military activities and increased political tensions in the region which present an increasing inadvertent risk to US civil aviation operations due to the potential for miscalculation or misidentification."
Tensions have risen in recent days, with concerns about a potential US-Iran conflict. Earlier this week, the United States pulled some diplomatic staff from its embassy in Baghdad following weekend attacks on four oil tankers in the Gulf.
Washington has increased economic sanctions and built up its military presence in the region, accusing Iran of threats to US troops and interests. Tehran has described those steps as "psychological warfare" and a "political game."
On Friday, a defiant Iran said it could "easily" hit US ships.