Saudi-led coalition forces in Yemen said an "unidentified projectile" had targeted Riyadh's international airport Terminal 4 on Sunday, causing a fire.
An unspecified number of people were injured, the Saudi civil aviation authority said, adding it was still assessing the damage.
The coalition also said Saudi air defences had intercepted a cruise missile in the vicinity of Riyadh's King Khalid International Airport. It later added that a drone had been intercepted and destroyed in the kingdom's Eastern Province.
The strikes have exposed vulnerabilities in Saudi defence capabilities as the kingdom wages an air campaign against the Iran-aligned Houthis, who are fighting a ground war in Yemen against the Saudi-backed Yemeni government.
The airport has been closed since Saturday's attack, although an international energy conference went ahead in Riyadh on Sunday.
In a televised speech on Sunday, Houthi military spokesperson Yahya Saree claimed responsibility for Saturday's attack and said the group had attacked the airport in Dammam in Saudi Arabia's Eastern Province and two facilities of Saudi oil giant Saudi Aramco.
The Saudi civil aviation authority confirmed the strike on Dammam's King Fahd International Airport late on Sunday, adding that "damage assessments and safety inspections of airport facilities are under way".
An eyewitness aboard a taxiing aircraft at the Dammam airport told Reuters that around 8:30pm on Sunday, they saw a projectile strike the tarmac beside several parked aircraft, causing a fire.
The witness said the aircraft returned to the gate, where passengers disembarked and were told to leave the airport.
Flight-tracking website Flightradar24 showed several delays and cancellations on Sunday evening for arrivals and departures at Dammam airport, which serves the capital of the oil-producing region and is the kingdom's third-largest airport.
The Houthis earlier on Sunday had renewed their warning to airlines, airport workers and travellers against using Saudi airports.
"We urge everyone to take our warnings seriously, and Saudi Arabia bears responsibility for any failed interceptions," the group said.
Saudi Arabia has stepped up its military involvement in Yemen in recent weeks, launching strikes against the Houthis and backing a Yemeni government counteroffensive after the Houthis seized strategic territory along the Red Sea coast last month.
The Houthis said on Sunday that Saudi Arabia carried out 124 air strikes in Yemen in the past 24 hours, including against the capital Sanaa and the group's stronghold Saada.
Yemen's Houthi-run foreign ministry said that further Saudi military action in Yemen would trigger a stronger response, adding that its actions would be guided by the principle of reciprocity.
"Unless the Saudi enemy stops its aggression and interference in Yemen, worse is yet to come, God willing," the ministry said in statements carried by Houthi-run Al Masirah television.
US President Donald Trump said the US was considering joining Saudi strikes on the Houthis in the conflict, a spillover from the wider war with Iran that the US and Israel launched in February.
Saudi authorities notified parents that in-person classes at all schools in Riyadh would be suspended and shifted to remote learning from Sunday until Thursday.
In Saturday's attack, the dead included four Saudis and two Bangladeshis, as well as nationals of the United States, Jordan, Palestine, Syria, Sudan and Egypt, Saudi authorities said. India's embassy in Riyadh said on Sunday one of its citizens injured in the attack had died, adding to the initial death toll of 12.
Four people were killed in the two previous attacks on the airport earlier in the week.
