Yemen's Iran-backed Houthi rebels said they had launched missile and drone salvos against Saudi Arabia's oil facilities on Saturday, as fighting between regional allies of the United States and Iran intensified on a new front.

In a video statement, military spokesman Yahya Saree said the rebels targeted sites operated by the Saudi oil giant Aramco in Jizan and Yanbu, threatening to expand the group's response if attacked by the Gulf monarchy.

Earlier, the rebels' media had said a strike on Jizan had sparked fires. A video circulating on social media, and verified by AFP, showed dark clouds rising above a refinery belonging to Aramco in the city.

Saudi Arabia made no direct comment on the attack but the kingdom's civil defence issued warnings for Jizan, on the kingdom's southwest coast, as well as in Yanbu to the north.

A surface-to-air battery operated by Greek personnel in Saudi Arabia downed two ballistic missiles and later a drone launched from Yemen targeting Yanbu on Saturday morning, the Greek air force press office said.