The leadership of the Houthi movement has vowed to fire more missiles into Saudi Arabia unless it stops bombing Yemen.

The warning comes after missiles crashed into Riyadh overnight causing casualties in the Saudi capital for the first time.

Saudi security forces said they shot down three missiles over Riyadh shortly before midnight. Debris fell on a home in the capital, killing an Egyptian resident and wounding two other Egyptians.

Air defences also repelled missiles fired at the southern Saudi cities of Najran, Jizan and Khamis Mushait, Saudi-led coalition spokesman Colonel Turki al-Malki said.

A top Houthi leader hailed the attack, which took place on the eve of the third anniversary of the entry into the Yemen war by Saudi Arabia and its Arab allies.

If they want peace, as we have said to them before, stop your air strikes and we will stop our missiles - Saleh al-Samad, Houthi leader

"We praise the successful advance of military capabilities," Houthi political council chief Saleh al-Samad told a crowd of tens of thousands of supporters in the Yemeni capital Sanaa.

"If they want peace, as we have said to them before, stop your air strikes and we will stop our missiles," he said. "If you continue your air strikes we have a right to defend ourselves by all means available."

The war in the Arabian Peninsula's most impoverished country, which pits a coalition of Sunni Arab states friendly to the West against a Shia armed movement allied to Iran, has unleashed one of the world's worst humanitarian crises.

The Houthis control the north of Yemen, including the capital Sanaa. Saudi Arabia and its allies have been fighting on behalf of an exiled government with a foothold in the south.

Explosions

Khattab Gamal, a 27-year-old Egyptian electrician who lived in the Riyadh house hit by the debris, told Reuters loud explosions awoke him and his 15 housemates.

"We knew something fell on the room where Abdulmuttalib was asleep. There were three others in the same room with him. All were asleep at the time of the explosion. They all rushed and ran out and then we realised he was missing.

"We kept looking for him and realised he was still inside, we went back and tried to enter the room and save him but we couldn't," he said by telephone. "There was a lot of dust, and the smell was suffocating.... A few minutes later the civil defence came and got him out, but he was already dead."

The Saudi-led coalition has launched thousands of air strikes on Yemen in the past three years, some of which have hit hospitals, schools and markets, killing hundreds of civilians while bringing Riyadh little closer to military victory.

The kingdom has said hundreds of its soldiers and civilians were killed in Houthi mortar and short-range missile attacks across their rugged southern border.

The United Nations says 10,000 people have died in the conflict so far, and millions face potential famine and disease because of disruption to food and medical supplies.

Leadership of Houthi movement sit behind bulletproof glass during rally (Reuters)

Around 22 million civilians, or 75 percent of Yemen's population, require humanitarian aid, according to latest UN data. The conflict has caused the worst cholera outbreak in modern history, with over 1 million reported cases.

Last year, when the Houthis fired missiles at Riyadh which were intercepted without doing damage, the Arab coalition responded by shutting Yemen's airports and ports, a blockade that the United Nations said raised the prospect of mass starvation before it was partially lifted.

Western countries have urged Saudi Arabia and its Gulf Arab allies to protect civilians and find a quick end to the war. But they also support Riyadh's argument that it needs to defend itself from cross-border strikes and limit the spread of Iranian influence in territory overlooking essential trade routes.

The Saudi military depends on service contracts with Western arms companies to keep its planes flying.

Saudi Crown Prince Mohammed bin Salman discussed the war with US President Donald Trump during a visit to the White House last week and with British Prime Minister Theresa May in London the previous week.

Saudi Arabia viewed the 2014 takeover of Sanaa by the Houthis as part of a regional strategy by arch-foe Tehran to encircle it. Independent UN experts reported to the Security Council in January that Houthi missiles they had examined and other military equipment were manufactured in Iran.

The Houthis deny they are Iranian pawns, and say their spread throughout Yemen is a national revolution against corrupt government officials and Gulf Arab states in thrall to the West.

Diplomats and Yemeni political officials reported this month that the Houthis and Saudi Arabia were conducting secret peace talks after years of UN-mediated dialogue yielded no results.