Saudi Arabia's energy minister has vowed a "serious" response to the deadly attacks on the kingdom's airports and oil and gas facilities by Yemen's Iran-backed Houthi movement.

"The events of recent weeks are serious. Our response must be equally serious," Prince Abdul Aziz bin Salman told the WPC Energy Congress in Riyadh.

On Sunday, a Pakistani man was killed in an attack on a terminal at the capital's King Khalid International Airport, Saudi authorities said. It came a day after a Houthi missile hit another terminal, killing 13 people and forcing its closure.

The Houthis said they launched the attacks in retaliation for "brutal Saudi aggression" against areas they control in western Yemen.

The Houthi-run health ministry said a child was killed and six other people were injured in a Saudi air strike on a home in the capital, Sanaa, on Sunday.

A Saudi-led coalition has been providing air support for Yemeni pro-government forces battling the Houthis on Yemen's Red Sea coast and other areas.

Yemen has been devastated by a civil war that began in 2014, when the Houthis ousted the government from Sanaa. The conflict escalated in 2015, after the Saudi-led coalition intervened in an attempt to restore the government's rule.

A four-year-old informal ceasefire began to unravel in July, when the Houthis announced a "maritime embargo" against Saudi Arabia and began missile and drone attacks on Saudi airports, oil facilities and tankers in the Red Sea.

The Houthis said they were retaliating for what they say is a Saudi blockade of ports and airports in their territory, as well as an air strike on Sanaa airport that they blamed on the kingdom. The Yemeni government claimed it was behind that strike, saying it was trying to prevent an unauthorised Iranian plane from landing.

Last month, the Houthis launched a surprise offensive along Yemen's south-western Red Sea coast and ousted pro-government forces from areas overlooking the Bab al-Mandab Strait, at the southern end of the Red Sea.

They said they posed no threat to international shipping passing through the waterway but that they would continue to target vessels from Saudi Arabia.

However, the seizure of the strait contributed to a surge in global oil prices because Saudi Arabia had been relying on the Red Sea for oil exports after the US and Israel's war with Iran effectively closed the Strait of Hormuz in the Gulf.

Last week, the Yemeni government announced the start of a new offensive aimed at retaking all territory held by the Houthis.

Pro-government forces said they were quickly able to retake areas around Bab al-Mandab with the help of intense Saudi air strikes, but the Houthis denied losing any territory.