"The US ambassador to the UN, Susan Rice, sent a letter to Mohammad Khazaie, Iran's UN representative, which was conveyed by the Swiss ambassador, and finally Iraqi President Jalal Talabani delivered its contents to officials" in Iran, the official IRNA news agency quoted Ramin Mehmanparast as saying.
"We are in the process of studying the letter and if necessary we will respond."
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The United States has had no diplomatic relations with Iran since shortly after the 1979 Islamic revolution, and Swiss diplomats handle US interests there.
On Friday, the New York Times, citing unnamed US officials, reported that Washington had used a secret channel to warn Iran's supreme leader Ayatollah Ali Khamenei that closing the narrow strategic waterway would cross a "red line" and provoke a response.
Tehran threatened to close the strait - a chokepoint for one fifth of the world's traded oil - late last month, in the event of a military strike or severe tightening of international sanctions over its controversial nuclear program.
Washington is beefing up its naval presence in waters just outside the Gulf in response to the threats.
The US officials did not provide details about the covert communication channel, except to say that it was separate from the Swiss government.
Washington and its allies have stepped up increasingly harsh sanctions on Iran over its nuclear enrichment program, which they charge is part of a secret drive to develop nuclear weapons.
Iran insists its atomic ambitions are entirely peaceful and has vowed to retaliate against any strike on its facilities.
Tensions again flared following Wednesday's killing of an Iranian nuclear scientist in a bombing Tehran blamed on US and Israeli intelligence services. US officials have denied any involvement.
Iran's Revolutionary Guards have announced new naval maneuvers in the Strait of Hormuz within the next few weeks, underlining Tehran's threat to close the channel linking the Gulf and the Arabian Sea.