Washington DC - President Donald Trump declared Monday he will hold Iran directly responsible for any future attacks by Yemen's Tehran-backed Houthi rebels, who have targeted US and other foreign ships in the Red Sea.

"Every shot fired by the Houthis will be looked upon, from this point forward, as being a shot fired from the weapons and leadership of IRAN, and IRAN will be held responsible, and suffer the consequences," Trump posted on his Truth Social platform.

While the US has been carrying out strikes on Houthi targets for months, Trump's comments were unusually pointed at Iran, whom he is also pressuring over nuclear talks.

He spoke after the first US strikes on Yemen of his new term killed 53 people and wounded 98 on Saturday.

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In response, the Houthis claimed two strikes on a US aircraft carrier and rallied thousands at protests in parts of Yemen under their control.

The US struck the Houthis over their repeated attacks on Red Sea shipping vessels, which have put a major strain on the vital trade route.

The Houthis have said they are carrying out the attacks in solidarity with Palestinians in Gaza, where Israel is waging a war with US support.

"Any further attack or retaliation by the 'Houthis' will be met with great force," Trump also said in his post, adding that "Iran has played 'the innocent victim'" in the conflict.

On Monday, in the Pentagon's first formal press briefing of this Trump presidency, officials said US strikes against the Houthis were continuing in order to degrade their ability to plan and conduct attacks, and that Iran was on notice from Trump.

"All options are on the table at this time," spokesman Sean Parnell told reporters when asked whether the president was considering military action against the Islamic Republic.

He also said the US will continue to use "overwhelming lethal force" until it achieves its objectives.

"There is a very clear end state to this operation, and that begins the moment that the Houthis pledge to stop attacking our ships and putting American lives at risk," Parnell said.

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US Air Force Lieutenant General Alexus Grynkewich told the briefing more than 30 Houthi targets were hit Saturday, including "terrorist training sites" and weapons manufacturing facilities.

The weekend targets "also included a number of command-and-control centers, including a terrorist compound where we know several senior Houthi unmanned aerial vehicle experts were located," he added.

"Today, the operation continues, and it will continue in the coming days until we achieve the president's objectives."

Houthi media reported that fresh US air strikes on Monday targeted rebel-held Hodeida on Yemen's western coast.

Before this weekend's targeting of the US carrier group, the Houthis had not claimed attacks in the Red Sea and Gulf of Aden since January 19, when a ceasefire in Gaza began.