A missile fired by Iranian-backed Yemeni rebels hit a Saudi airport on Wednesday, wounding 26 people and ratcheting up regional tensions just as worldwide efforts to avert escalation get underway.
He added that the coalition would take "urgent and timely measures to deter this terrorist militia".
"A total of 26 civilian passengers of different nationalities were injured by the projectile, including three (3) women (Yemeni, Indian, Saudi) and two (2) Saudi children", he added. Eight have been hospitalized and the rest sustained minor injuries.
Saudi Arabia's civil aviation authority said on Wednesday afternoon that air traffic had returned to normal at the airport.
"It also proves that these terrorist militias have received new weapons, and that the Iranian regime continues its support and practice of cross-border terrorism and the continuing violation of relevant Security Council resolutions, including Resolution 2216 and Resolution 2231".
A coalition statement said a projectile hit the arrivals hall at airport, causing material damage.
The coalition, which has been fighting the Houthis in Yemen, said it would make a "firm" response.
The US Embassy in the Kingdom said on Twitter that it condemns "in the strongest possible terms the Houthi attack on innocent civilians at Abha airport".
The coalition said the attack could amount to a war crime.
In May, the Shiite Huthi rebels also carried out twin drone attacks on the kingdom's strategic east-west oil pipeline, forcing a two-day closure of the main diversionary route for Saudi exports avoiding the Gulf.
The U.S., meanwhile, blames Iran for a mysterious attack on oil tankers off the coast of the United Arab Emirates and sent an aircraft carrier and B-52 bombers to the region, along with hundreds more troops to back up the tens of thousands already deployed in the region.
The rebels said they had targeted the King Khalid airbase near Khamis Mushait.
Al-Malki said that the militias claiming full responsibility for this terrorist act constitutes "a clear and full recognition of the responsibility of targeting civilian and civilian objects that are subject to special protection under global humanitarian law".
"The Houthis ... are saying these kind of attacks are revenge for Saudi Arabia's escalation and their attacks on civilian areas over the past four years", al-Attab said.
There has been a spate of cross-border attacks by the rebels in recent weeks which have coincided with reports of intensified coalition strikes on rebel strongholds on the other side of the border.