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The Saudi-led coalition battling Houthi rebels in Yemen closed the country's air, sea and land borders on Monday and accused Iran of being behind a missile attack on Riyadh this weekend, warning the strike "may amount to an act of war".

Saudi Arabia intercepted and destroyed the ballistic missile, which was launched from Yemen as rebels appeared to escalate hostilities, near Riyadh's international airport on Saturday.

The missile was the first aimed by the rebels at the heart of the Saudi capital, underscoring the growing threat posed by the raging conflict.

"The leadership of the coalition forces therefore considers this... a blatant military aggression by the Iranian regime which may amount to an act of war," the official Saudi news agency SPA said in a .

Smouldering debris landed inside the King Khalid International Airport, just north of Riyadh, after the missile was shot down but authorities reported no major damage or loss of life.

Yemen's complex war pits the Saudi-backed government of President Abd Rabbo Mansour Hadi against former president Ali Abdullah Saleh and his Iran-backed Houthi rebel allies.

The Saudi statement said that the borders were being closed "to fill the gaps in the inspection procedures which enable the continued smuggling of missiles and military equipment to the Houthi militias loyal to Iran in Yemen".

Despite the temporary closure of the air, sea and land ports, Saudi would protect "the entry and exit of relief and humanitarian personnel".

"The coalition... affirms the kingdom's right to respond to Iran at the appropriate time and in the appropriate form," it added.

Iran has backed the Houthi rebels, but denies arming them. There was no immediate response from Iran over the Saudi threat.

The war in Yemen has claimed more than 10,000 lives and driven the Arab world's poorest country to the brink of famine.