Yemen's Iran-backed Houthi rebels claimed a missile attack on Saudi Arabia on Saturday as fighting between regional allies of the United States and Iran intensified on a new front.

Houthi media said the rebels targeted the Saudi city of Jizan on the Red Sea and Saudi's civil defence issued warnings in the area on the kingdom's southwest coast as well as in Yanbu to the north.

A post by Ansarollah media on Telegram said the strike had sparked fires in Jizan and a video circulating on social media, and verified by AFP, showed dark clouds rising above a refinery belonging to Saudi oil giant Aramco in the city.

Earlier, the Iran-backed group accused US ally Saudi Arabia of a "dangerous escalation" after Riyadh struck Houthi targets on Friday.

A Yemeni security source told AFP a naval base in the port city of Hodeida and a military camp on Kamaran Island were among the Saudi targets.