Three people have been killed in attacks on Saudi Arabia airports over two days, authorities said, as flare-up of fighting spilled across the Yemen border into the kingdom.

Two people were killed and 28 wounded in an attack at Abha International Airport, Saudi Arabia's General Authority of Civil Aviation (Gaca) said in a statement on Wednesday.

In a separate incident, one person was killed and eight were wounded in an attack on King Khalid International Airport in Riyadh, Saudi Arabia's capital, it added.

The attacks, which the Houthis have claimed responsibility for, mark an escalation in the renewed war between the Saudi-backed government forces and the Iran-backed Houthis in Yemen.

The two airports were attacked on 6 and 7 October, according to Gaca, which did not specify when each airport was hit.

Two women, of Moroccan and Algerian nationalities, were killed during the Abha airport attack, near the Yemen border, according to Gaca.

Meanwhile, a male resident of Sudanese nationality was killed at King Khalid airport, it added.

The country's civil aviation authority did not name who was responsible for the attacks, but Houthi military spokesperson, Yahya Saree, said its armed forces had attacked both Saudi Arabia airports with ballistic missiles and drones.

The Houthi military spokesperson also said the Houthis attacked Aden's International Airport in Yemen on Wednesday. The airport is a main international gateway for parts of Yemen outside of Houthi control and has been repeatedly targeted when fighting erupts in the country.

Saree said the two attacks on Saudi Arabia's airports were in "response to the Saudi aggression against our country" which saw "60 airstrikes and missile attacks in the past 24 hours".

The civil war in Yemen has worsened in recent weeks, after the Houthis, who control most of the country's north-west, seized strategically important stretches of the Red Sea coast in a rapid offensive.

That included the port of Mokha on the Bab al-Mandab Strait, which is the narrowest point of the Red Sea and a chokepoint for global shipping.

But Yemeni pro-government forces backed by Saudi Arabia have since said they had "secured" the Bab al-Mandab Strait at the southern end of the Red Sea.

They also declared an all out war in an effort to take all territory held by the Houthis.

In a statement issued late on Wednesday, the official spokesperson for the Saudi-led coalition said the Houthis' attacks on Saudi Arabia's airports "will not go unpunished".

The spokesperson said the Saudi coalition had targeted more than 80 Houthi military sites across "governorates of Saada, Al Hudaydah, Al Jawf and Ma'rib".

The Saudi-led coalition formed in 2015 after Arab countries joined forces to stop the Houthis taking over Yemen from the country's internationally recognised government.

A temporary ceasefire was brokered in 2022 after years of air strikes and ground fighting led to the deaths of hundreds of thousands of people, triggering one of the world's worst humanitarian crises.

UN Secretary General Antonio Guterres has condemned "the continued Houthi cross-border attacks" on Saudi Arabia and said he was "deeply concerned by the sharp escalation in fighting".

Hundreds of people have reportedly been killed on both sides since the latest Houthis' advance.

The UN said on Wednesday more than 200,000 people have been displaced by the escalation.