Yemen's Iran-backed Houthi media Ansarollah said Tuesday that the rebels hit targets in Saudi Arabia, as they press an offensive to seize territory near the Bab al-Mandab Strait.

The Houthis had accused Riyadh on Monday of carrying out strikes around the country, including the deadly bombardment of a prison.

"Yemeni drones and missiles pound the Saudi enemy," Ansarollah wrote on Telegram.

It said in a separate post that the strikes hit Abha International Airport, King Khalid air base and facilities belonging to state-owned oil giant Aramco in Abha and Jizan.

Saudi Arabia did not immediately comment on the report.

Days of fighting near the Red Sea coast have left more than 300 people dead and displaced hundreds of families as the Houthis try to capture land bordering the Bab al-Mandab Strait.

The strait forms the southern entrance to the Red Sea, a shipping artery that has become vital for Saudi oil exports amid Tehran's blockade of the Strait of Hormuz since the start of the US-Iran war on Iran.

Almasirah quoted Hassan Saboula, director-general of civil defence in Jawf province, saying that Monday's prison strike killed 11 people and left 20 inmates missing under the rubble.

Saba news agency, which is affiliated with the Houthi movement, reported earlier that a child visiting the facility was among the dead.