The facility reportedly belonged to the oil giant Saudi Aramco. Houthis reported the attack on their website saying dozens of Sudanese soldiers had been killed and armoured vehicles destroyed.
The Houthi-run al-Masirah TV channel said the ballistic missiles targeted the Saudi Defense Ministry in Riyadh, among other targets in the kingdom's capital.
Saudi Aramco said on Wednesday that its facilities in the southwestern province of Jizan were operating "normally and safely".
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Until recently, the GPC was headed by former Yemeni President Ali Abullah Saleh, who was killed late previous year outside capital Sanaa by members of the Shia Houthi militia group. Saudi state media said air defences had intercepted a missile over the capital.
The attack on Wednesday marked the fourth time in five months that missiles have flown over Riyadh, as the Houthis step up efforts to demonstrate they can reach the Saudi capital, and threatens to escalate a regional rivalry between Iran and Saudi Arabia.
The company is building a 400,000-barrel-per-day refinery in Jizan, part of a new economic city on the Red Sea, which is expected to become fully operational in 2019.
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Spokesman for the Arab Coalition forces fighting in Yemen, Col. More than 10,000 Yemenis have died in the conflict and millions in the impoverished country have been pushed to the brink of starvation.
Meanwhile, the Saudi coalition fighting the Houthis in Yemen said its air defences shot down two unmanned drones in the south of the country.
Al-Masirah said the Houthis had also launched an attack with the same model of drone on the airport of Abha in neighbouring Asir province.
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The arms monitor Conflict Armament Research (CAR) said it had evidence showing the Qasef-1 and other Houthi kit was made in Iran and was not of indigenous design and construction "in contrast to Houthi statements".