"The attacks have halted air traffic at the airport," the spokesman said, though Riyadh hasn't commented on the claims yet.
The Houthis have been regularly targeting military and civilian positions across the border in Saudi Arabia in recent months. On Tuesday, the movement claimed that it had attacked the Abha airport, while the Saudi authorities dismissed the claim the same day.
The Saudi-led coalition is backing the government led by Abdrabbuh Mansur Hadi in its fight against the Houthi movement. The conflict has been ongoing for several years leading to a major humanitarian crisis.