Saudi Arabia claims to have shot down seven ballistic missiles fired by Yemen's Houthi militia, with debris killing a man in what was the first death in the capital Riyadh during the Saudi-led coalition's three-year military campaign in Yemen.

Saudi forces destroyed three missiles over north-eastern Riyadh shortly before midnight, as well as others fired at the southern cities of Najran, Jizan and Khamis Mushait, the coalition said in a statement carried by state news agency SPA.

SPA said one man died and two other people were injured by "falling debris" in Riyadh.

However, videos shared online appeared to show a Saudi defence missile veering off course and crashing into a residential neighbourhood.

Reuters reporters in Riyadh heard several booms and saw smoke in the air.

Another witness said he saw a long stream of light followed by additional explosions.

In the al-Malqa neighbourhood, emergency personnel gathered near a crater in the ground and inspected shattered glass in nearby homes.

Iran' s state-owned Press TV claimed that a missile fired by Houthi rebels in Yemen had targeted King Khalid International Airport in Riyadh but was intercepted.

It also claimed airports in Abha, Najran and Jizan were also targeted by missiles fired from Yemen.

The casualties were the first in Saudi Arabia's capital since the Saudi-led war in Yemen began in March 2015, although previous rockets fired by the Yemeni rebels caused deaths in other parts of the kingdom.

Rivalry between Iran and Saudi Arabia

The attacks marked the third time in five months that missiles have flown over Riyadh, as the Houthis step up efforts to demonstrate they can reach the Saudi capital.

The missile attacks threaten to escalate a regional rivalry between Iran and Saudi Arabia.

Houthi ballistic missiles have increased in range over time, with the first one targeting Riyadh fired in May last year, according to the United Nations.

The Saudi-led coalition of Gulf Arab states launched military operations against the Houthis in Yemen in March 2015, after the Iran-aligned Shiite militia seized the Yemeni capital Sanaa and forced President Abd Rabbu Mansour al-Hadi to flee.

Riyadh saw the move as a regional power grab by arch-foe Iran, although the Houthis deny any help from Tehran.

Saudi Arabia has called Iran's alleged supply of rockets to the Houthis "direct military aggression."

The United States, which provides support to the coalition, has also displayed what it said were Iranian-made weapons supplied to the Houthis, calling them conclusive evidence that Tehran was violating UN resolutions.

The conflict in Yemen has killed more than 10,000 people and displaced more than 2 million, unleashing a humanitarian crisis in the Arabian Peninsula's poorest country where nearly 1 million people have been infected with cholera.