The announcement came as Washington said it had destroyed radar sites controlled by the Iran-backed Huthi rebels in Yemen, in response to failed missile attacks on its warships in the Red Sea.
However, the two Iranian destroyers were dispatched on October 5, before the incidents involving the US, the conservative-linked Tasnim news agency reported.
Their mission takes them to the Gulf of Aden and the Bab al-Mandeb Strait between Yemen and the Horn of Africa "to protect merchant vessels against pirates", before heading on to Tanzania and possibly South Africa, Tasnim said.
It was not clear if the destroyers had already arrived in the Gulf of Aden.
The US cruise missile strikes today were Washington's first direct action against the Huthi rebels, although it has provided logistical support to the Saudi-led coalition battling the insurgents.
The USS Mason, a destroyer, was targeted yesterday by a missile fired from rebel-held territory which crashed into the ocean before reaching its target.
The Mason and the USS Ponce, an amphibious staging base, had already been targeted on Sunday by two missiles that also fell short.
Iran supports the Shiite Huthis, but denies supplying arms and has fiercely criticised the bombing campaign led by the Saudis.
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