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The message is mainly directed at U.S. naval forces in the Persian Gulf that regularly encounter Iranian naval forces in those waters.

"We are watching, and ensuring disciplined restraint on the part of our naval forces," one official told CNN. The U.S. military's concern is that Iranian naval forces could engage in some activity in the Gulf waters that could be a "triggering event," that U.S. forces might been compelled to react to.

The second official said there is also great concern that Iran not misunderstand this message calling for restraint, and think the United States is lowering its guard.