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Yemen's Houthi rebels made a show of strength in the capital Sanaa Monday, hours after missiles were fired at Saudi Arabia's capital and to mark the anniversary of Riyadh's intervention in the war-torn country three-years-ago.

Hundreds of thousands of Houthi supporters paraded through Sanaa, waving Yemeni flags, chanting slogans and brandishing portraits of the Zaydi-Shia group's leader Abdelmalek al-Houthi.

Schools and government buildings were closed in the Houthi-controlled capital as demonstrations were held marking the start of air strikes by the Saudi-led coalition against the group in March 2015.

A message was broadcast at the parade by Hassan Nasrallah with the Lebanese militia leader praising the "steadfastness" of the "Yemeni people" against the Saudi intervention force.

The crisis in Yemen began in September 2014, when the Houthis and supporters of former President Ali Abdullah Saleh took over the capital forcing the government to flee south.

Saudi Arabia, the UAE, and some other Arab nations launched an intervention force in 2015 to back the government of President Abd Rabbo Mansour Hadi.

Ibtisam al-Mutawakel, head of the Houthi's cultural committee, told AFP the missiles targeting Saudi Arabia were intended to be a message to the kingdom's leadership from the rebels.

"No one can speak on behalf of the Yemeni people. People taking to the streets today is the real voice," Mutawakel said. 

"As for the missiles, those are the message of our army and popular committees [Houthis] to the enemy."

The missile attack on Riyadh, Sunday evening, left one person dead from falling shrapnel.

Riyadh said the missiles were intercepted by its air defence systems, but the incident was another embarrassment for Saudi Arabia.

Rebel missiles reached the capital in November drawing anger from the Saudi leadership who blamed Iran for providing the weapons to the Houthis.

Saudi Arabia's US-made air defence systems have come under the spotlight for their failure to intercept the missiles earlier.

Houthi rebels confirmed via al-Masirah TV they were responsible for the missile barrage. The group said three missiles targeted Riyadh's King Khalid International Airport, two were aimed at Jazan and one apiece at Najran and Khamis Mushait. 

Saudi authorities said an Egyptian citizen was killed in the capital Riyadh from the falling shrapnel.

The Saudi-led coalition condemned the strikes. 

"This aggressive and hostile action by the Iran-backed Houthi group proves that the Iranian regime continues to support the armed group with military capabilities," coalition spokesman Turki al-Malki said. 

Yemen's war has cost around 10,000 lives and created one of the world's worst humanitarian crisis.

A blockade by the Saudi-led coalition has threatened the country with starvation and disease, while air strikes continue to kill and maim civilians.

Agencies contributed to this story.