The Riyadh-led military coalition fighting the rebels said the two officers ejected from the plane before it crashed in northern Al-Jawf province Friday but that the rebels opened fire at them in "violation of the international humanitarian law".

"The joint forces command of the Coalition holds the terrorist Huthi militia responsible for the lives and wellbeing of the Tornado air crew under the international humanitarian law," the coalition said in a statement released by the official Saudi Press Agency late Saturday.

The statement did not specify whether the crew had survived or if they had been captured after the plane crashed in Huthi-controlled territory.

The coalition also did not elaborate on the reasons for the crash.

But if Huthi involvement is confirmed, the rare downing of a coalition warplane would mark a setback for a military alliance known for its air supremacy and signal the rebels' increasingly potent arsenal.

The rebels released footage of what they called the launch of their "advanced surface-to-air missile" and the moment it purportedly struck the jet in the night sky, sending it crashing down in a ball of flames.

The crash triggered air strikes in the area where the plane went down, an apparent Saudi-led retaliation that the UN said left 31 civilians dead and 12 others wounded.

The rebels reported multiple coalition air strikes in the area, adding that women and children were among the dead and wounded, according to rebel television station Al-Masirah.

The coalition conceded the "possibility of collateral damage" during a "search and rescue operation" at the site of the jet crash.

The coalition force has been widely criticised for the high civilian death toll from its bombing campaigns in Yemen, which has prompted some Western governments to cut arms deliveries to the countries taking part.

The coalition intervened against the Huthis in 2015, in a conflict that has killed tens of thousands of people, most of them civilians, and sparked what the United Nations calls the world's worst humanitarian crisis.