The Houthis, a key part of Iran's so-called "axis of resistance", have so far refrained from joining the war sparked by US-Israeli strikes on Iran, which has engulfed much of the region.

"As the people of Yemen, we repay loyalty with loyalty," the Houthi leader said in a speech broadcast by the rebels' Al-Masirah channel affiliated with his movement.

"Any development in the battle that requires a military response, we will promptly undertake it... just as we did in previous rounds," the leader said.

Houthi did not specify what kind of military action his movement might undertake.

"Our position is clear and explicit against America and Israel, and we harbour no hostile intentions toward any Muslim country," he said, in what appeared to be a reference to countries in the Gulf.

Yemen is strategically located on the Red Sea coast, and during the Israel-Hamas war in Gaza it brought shipping to a near-standstill by launching missiles at vessels it said were affiliated with Israel, as well as towards Israel itself.

This time, shipping through the vital Strait of Hormuz in the Gulf has been largely blocked, with Iran warning vessels from countries it considers hostile that transit is unsafe.

Following the outbreak of the war, the world's biggest crude exporter Saudi Arabia began pumping millions of barrels of crude a day through a massive pipeline connecting its energy installations to export terminals on the Red Sea.

The Petroline, as it is known, has helped cushion the war's blow -- allowing Saudi Arabia to bypass the Strait of Hormuz, where roughly 20 percent of global crude and liquefied natural gas supplies passed before the war.

But should the Houthis enter the fray, that could render the Red Sea alternative unsafe too.