Iran-backed Houthi rebels in Yemen have claimed a new ballistic missile attack on Riyadh's King Khalid International Airport, a day after Saudi Arabia said an attack on the airport killed one person.

The Saudi-led coalition said it intercepted two ballistic missiles launched toward Riyadh, along with a third fired toward Khamis Mushait near the Yemen border.

Saudi civil defence said debris from an interception damaged a kindergarten and a medical complex, with no casualties mentioned.

Saudi aviation authorities said three civilians were killed and 36 injured in Houthi attacks on the Riyadh and Abha airports on October 6 and 7.

The blasts pushed crude oil prices higher on supply-disruption fears, with Brent trading above $100 a barrel. The strikes marked the third straight day of attacks on Riyadh, and an oil and chemical tanker near Qatar was also hit on Wednesday, maritime monitors said.

Hundreds of flights to and from Riyadh were cancelled, according to flight-tracking data.