Houthi military spokesperson Yahya Saree said on Sunday the airport remained a "military target" and operations targeting the airport would continue, warning all airlines, airport staffers and travellers against using it.
Late on Saturday, King Khalid Airport said Terminal 1 would be designated for domestic flights and Terminal 2 for international flights operated by national carriers starting on Sunday.
Operations in the airport were halted on October 10, following an attack on the airport, claimed by the Houthis, that killed 13 people and wounded more than 300 others, the deadliest in the kingdom in more than a decade. The suspension of operations was extended two days later.
The Houthis have been firing ballistic missiles and drones at Saudi airports, ports and oil installations, turning US ally Saudi Arabia into a pressure point in the wider war.
Saudi Arabia has recently stepped up its military involvement in Yemen, launching strikes against the Houthis and backing a government counteroffensive after the Houthis seized strategic territory along the Red Sea coast in September.
On Saturday Houthi rebels said they had launched attacks on Saudi oil facilities and airports while the Saudi-led coalition fighting the group says it downed two missiles as clashes between the two sides intensify.
Yemen's Saudi-backed government said the Houthis also fired three ballistic missiles at coast guard sites in the southern Yemeni port city of Aden.
Saudi authorities did not comment directly on the Houthi statements although they reported missile debris falling near the site of one of the purported oil targets.
It was not immediately clear if any of the reported attacks had hit their targets in the kingdom or had been intercepted.
Saree said the group targeted King Khalid International Airport, an Aramco facility in Yanbu, the Rabigh oil refinery, crude oil pumping stations and the East-West Pipeline.
He also said the Iran-aligned group targeted King Fahd International Airport in Dammam, an airport in Najran and an air base in Khamis Mushait.
Saree said the latest hits were in retaliation for Saudi attacks on Yemen, putting them at 100 air strikes over the past 24 hours.
Houthi-linked media reported deadly air strikes by the Saudi coalition on the Houthi-ruled capital Sanaa.
At least four people were killed and several others injured in a strike on a house in the Asr area in the western part of Sanaa, the Houthi-affiliated television al-Masirah reported.
The Houthi-controlled news agency Saba meanwhile said Saudi jets had targeted a cement factory in the Hamdan district in Sanaa, killing and injuring an unspecified number of civilians.
Al-Masirah later reported that eight were killed and 10 others injured in this attack.
The renewed fighting has shattered a 2022 United Nations-brokered truce that largely halted cross-border attacks between the Saudi-led coalition, which backs Yemen's internationally recognised government, and the Houthi rebels, who control Sanaa.
with DPA