Washington DC - President Donald Trump on Wednesday said Yemen's Iran-backed Houthi rebels "will be completely annihilated," warning Tehran against continuing aid for the group amid an ongoing US military campaign against them.

"Iran must stop the sending of these Supplies IMMEDIATELY. Let the Houthis fight it out themselves. Either way they lose, but this way they lose quickly," Trump posted on his Truth Social platform.

The Republican referenced reports that Iran "has lessened its intensity on Military Equipment and General Support" for the Houthis, though added that "they are still sending large levels of Supplies."

"Tremendous damage has been inflicted upon the Houthi barbarians, and watch how it will get progressively worse – It's not even a fair fight, and never will be. They will be completely annihilated!" his post continued.

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The US began launching heavy strikes against Yemen's Houthis on Saturday. Washington has pledged overwhelming force until the rebels stop firing on key shipping routes in the Red Sea and Gulf of Aden.

Part of Iran's "axis of resistance" against the US and Israel, the Houthis have been hampering the trade lane since the start of the Gaza war, claiming solidarity with Palestinians.

The Houthis on Wednesday claimed to have carried out an attack on American warships in the Red Sea, the fourth strike they took credit for in the past three days.