A US defense official said the altercation took place starting around 1930 GMT on Saturday. It was unclear how many of the surface-to-surface missiles were fired at the USS Mason, USS Nitze and USS Ponce.
The USS Mason destroyer, which was sailing in international waters off Yemen's coast earlier this week, used unspecified countermeasures against the incoming missiles, the official said.
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Officials have stressed that Washington wants to avoid getting embroiled in yet another war in an already volatile region where America is to varying degrees waging wars in Afghanistan, Iraq, Libya and Syria.
On Thursday, the US Navy launched five Tomahawk cruise missiles at three mobile radar sites in Huthi-controlled territory on Yemen's Red Sea coast, after the Iran-backed rebels blasted rockets at the USS Mason twice in four days.
The military insists these moves are taken out of self-defense. The Huthis have denied conducting the attacks.
Though the United States is providing logistical support to a Saudi-led coalition battling the rebels, Thursday's launches marked the first time Washington has taken direct action against the Huthis.
But the US strikes earlier this week did not take out Huthi missiles and, though the radar destruction makes it harder to aim the weapons, officials have warned rebels could still use spotter boats or online ship-tracking websites to find new targets.
The rockets fired at the USS Mason on Sunday and again Wednesday were believed to be the first time since 1987 that a US warship has been targeted by an incoming missile.
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