US airstrikes on Yemen have killed at least 18 people, according to the health ministry run by Houthi rebels.

US President Donald Trump ordered the air strikes on the capital Sanaa, promising to use “overwhelming lethal force” until the Iranian-backed Houthi rebels stop their attacks on shipping along a vital maritime corridor.

On Saturday the Houthis reported explosions in the capital of Sanaa and the northern province of Saada, the rebels’ stronghold on the border with Saudi Arabia, with more airstrikes reported in those areas early on Sunday.

Images online showed plumes of black smoke over the area of the Sanaa airport complex, which includes a sprawling military facility.

The Houthis also reported airstrikes early on Sunday on the provinces of Hodeida, Bayda, and Marib.

This image taken from video provided by the U.S. Navy shows an aircraft launching from the USS Harry S Truman in the Red Sea before airstrikes (US Navy/AP)

The health ministry said 13 of those killed were in Sanaa with five in Saada. At least 24 others were reported as injured.

A US official, speaking on the condition of anonymity, said this was the beginning of air strikes on Houthi targets that are expected to continue.

The Houthi media office said the US strikes hit a residential neighbourhood in Sanaa’s northern district of Shouab, including the Eastern Geraf neighbourhood which is home to Houthi-held military facilities and a headquarters for the rebels’ political bureau, located in a densely populated area.

The Houthis reported fresh strikes on the southwestern Dhamar province late Saturday. They said the strikes hit the outskirts of the provincial capital, also named Dhamar, and the district of Abs.

Mr Trump said on social media: “Our brave Warfighters are right now carrying out aerial attacks on the terrorists’ bases, leaders, and missile defences to protect American shipping, air, and naval assets, and to restore Navigational Freedom.

“No terrorist force will stop American commercial and naval vessels from freely sailing the Waterways of the World.

“These relentless assaults have cost the US and World Economy many BILLIONS of Dollars while, at the same time, putting innocent lives at risk.”

He also warned Iran to stop supporting the rebel group, promising to hold the country “fully accountable” for the actions of its proxy.

Mr Trump issued a new warning to Iran (AP)

The move comes two weeks after the American leader sent a letter to Iranian leaders offering a path to restarting bilateral talks between the countries on Iran’s advancing nuclear weapons programme that Mr Trump has said he will not allow to become operational.

Nasruddin Amer, deputy head of the Houthi media office, said the air strikes would not deter them and they would retaliate against the US.

“Sanaa will remain Gaza’s shield and support and will not abandon it no matter the challenges,” he added on social media.

The air strikes come a few days after the Houthis said they would resume attacks on Israeli vessels sailing in waters off Yemen in response to Israel’s blockade on Gaza.

There have been no Houthi attacks reported since then.

Earlier this month, Israel halted all aid coming into Gaza and warned of “additional consequences” for Hamas if their fragile ceasefire in the war is not extended as negotiations continue over starting a second phase.

The Houthis had targeted more than 100 merchant vessels with missiles and drones, sinking two vessels and killing four sailors, during their campaign targeting military and civilian ships between the start of the war between Israel and Hamas in late 2023 and January of this year, when this ceasefire in Gaza took effect.

The United States, Israel and Britain have previously hit Houthi-held areas in Yemen. Israel’s military declined to comment.