Yemen's Houthi group has said that Saudi warplanes had carried out 40 airstrikes across three Yemeni provinces over the past 24 hours, as intensified air operations and cross-border attacks marked a further escalation in the conflict.

In a statement posted on social media platform X on Wednesday (local time), Houthi military spokesperson Yahya Sarea said F-15 fighter jets taking off from the Khamis Mushait air base in southwestern Saudi Arabia carried out the strikes on the southwestern province of Taiz, northeastern Marib and northwestern Hajjah.

There was no immediate comment from Saudi authorities on the Houthi claim or information on possible casualties or damage from the reported strikes, Xinhua news agency reports.

The latest claim came as cross-border hostilities intensified. Earlier Wednesday, the Houthis said they had launched "dozens of ballistic missiles and drones" at Saudi Aramco facilities in the western Saudi city of Yanbu and several ballistic missiles at an air base in Khamis Mushait.

Sarea claimed the Yanbu attack caused large fires and extensive damage, while missiles targeting Khamis Mushait accurately hit their targets. Saudi authorities and Aramco have not commented on the claims.

Also on Wednesday, the Houthis claimed they had shot down a Saudi F-15 fighter jet with a locally made surface-to-air missile over Yemen's northeastern Marib province. Saudi Arabia has not commented on the claim.

The exchanges come amid a sharp escalation in Yemen since early September, with intensified airstrikes accompanying renewed ground fighting between the Houthis and government forces.

Heavy fighting continued on Wednesday over the Kahbub mountain range in the southern province of Lahj, which overlooks the strategic Bab al-Mandab Strait, a Yemeni military official told Xinhua. Five government soldiers and 10 Houthi fighters were killed and several others on both sides wounded in the clashes, the official said.

The Houthis have made major territorial gains along Yemen's Red Sea coast, capturing the strategic port city of Mocha on Sept. 10 before seizing Mayun Island at the heart of the Bab al-Mandab Strait on Sept. 11. The strait is a vital maritime chokepoint connecting the Red Sea with the Gulf of Aden.

Yemen's conflict erupted in late 2014 when the Houthis seized the capital, Sanaa, and much of northern Yemen, prompting a Saudi-led coalition to intervene in March 2015 in support of the internationally recognised Yemeni government.