Saudi authorities said Wednesday that three people were killed in attacks on two of the kingdom's international airports, including in the capital Riyadh, after Yemen's Houthis claimed to have fired on both transport hubs.

The Iran-backed fighters earlier took responsibility for a flurry of attacks that included firing a ballistic missile at Riyadh's King Khalid International Airport as the conflict deepens with Saudi Arabia, which backs Yemen's government.

"On Tuesday and Wednesday...Abha International Airport and King Khalid International Airport were subjected to attacks targeting their facilities," the kingdom's civil aviation authority said in a statement.

An Egyptian and an Algerian national were killed at Abha airport and a Sudanese national was killed at the airport in Riyadh, the agency said, with 36 people wounded in the attacks.

The Saudi-led military coalition that backs pro-government forces in Yemen said on X that it "destroyed the ballistic missile launch platform" used in the attack on Riyadh.

In a subsequent statement the coalition directly blamed Houthi forces and said it would retaliate.

"The brutal attacks by the Terrorist Houthi Militia on civilian and civilian objects in the Kingdom, most recently targeting (the two airports) will not go unpunished," it said on X.

The coalition said as a result it struck and destroyed 82 "legitimate military targets," including Houthi mountain-based ballistic missile facilities, command-and-control centers, communication systems and Houthi gathering sites.

The Yemeni group, which controls most of the country's northwest, is battling for territory against the Saudi-backed forces after the civil war reignited in July and it captured swathes of coastal land.

The fighting has displaced more than 200,000 people within the country, the United Nations said Wednesday.

Yemen's internationally recognised government this week declared a major counter-offensive and claims to have pushed Houthi fighters out of strategic areas on the Red Sea and the port city of Mocha.

But the Iran-backed Houthis say they are holding their territory, and military sources from both sides contacted by AFP have not reported any major changes on the ground.

Claims by the warring parties have been impossible to independently verify with the situation moving fast and access for journalists difficult.

- Flight diverted -

"Our armed forces have just targeted King Khalid International Airport in Riyadh with a ballistic missile. The strike was accurate, by God's grace, and led to a disruption of air traffic," Houthi military spokesman Yahya Saree said Wednesday on X.

The Saudi-led coalition said the missile was intercepted.

The Houthis also said they targeted a military supply convoy near the airport in Aden, the interim capital for Yemen's government.

The government's Saba news agency reported missiles and drones targeting that airport.

The agency cited transport authorities as saying one of the missiles landed near the runway minutes before the scheduled arrival of a flight from Cairo, which was forced to divert to Jeddah in Saudi Arabia.

Houthi drones and missiles also targeted Saudi Arabia's Abha airport and King Khalid Air Base in Khamis Mushait, spokesman Saree said, claiming they had "hit their targets accurately".

It is the second time this week Houthis claimed to have attacked Riyadh's main airport.

- 'Terrified' -

Saudi Arabia leads an international coalition fighting the Houthis since 2015, and is now trying to roll back the group's latest advance.

The coalition said Monday it was providing air support for the Yemeni government's counter-offensive.

After a four-year ceasefire, Yemen's civil war re-erupted in July. Last month the Houthis seized the entire western coastline along the Red Sea in the country's deadliest fighting in years.

New clashes Wednesday in Yemen's west left at least 62 combatants dead, including 37 Houthis, military sources from both camps told AFP.

Saba also reported the Houthis fired a missile at Taiz, a city held by government forces, wounding five civilians.

"We went out into the street to check on the wounded and saw young civilians who had been hit. The Houthi shell landed in the middle of the street, right in an area crowded with civilians," resident Al-Fateh al-Eisaei told AFP.

Yemen's government has announced a goal of retaking all Houthi territory -- home to most of the country's population, and much of it held for more than a decade.

The humanitarian crisis caused by the war has left most of the nation's population dependent on aid.

Mohammed, a 33-year-old charity worker who fled from Mocha to Aden, told AFP on Tuesday that "people there are terrified" of the Houthis.