In short:

At least 73 people, including children, have been injured in strikes on four Saudi Arabian cities.

Multiple oil facilities in the region have also been targeted.

What's next?

Houthi attacks on Saudi Arabia could disrupt Middle East energy supplies beyond the blockaded Strait of Hormuz.

Yemen's Houthis have attacked four cities in Saudi Arabia, setting fire to oil facilities and injuring more than 70 people.

The Iran-backed Houthis, who control most of Yemen's populated areas including the capital Sanaa, said they have launched an operation deep into Saudi territory, deploying drones and missiles to strike a Saudi air-base in the southern city of Khamis Mushait.

They also claim to have targeted spots belonging to Saudi Arabia's state oil company in nearby Abha, Najran on the Yemeni border and Jazan, a major Red Sea port city that houses a large refinery and power plant.

The move appears to be a major expansion of the war in the Midlde East which is now in its sixth month.

The reports of such large numbers of injured people suggested the attacks were among the biggest carried out against Saudi Arabia since the United States and Israel launched their war against Iran in February.

Saudi authorities said women and children were among the 73 people hurt in the attacks.

NASA satellite images showed a thick cloud of black smoke over the Jazan refinery and a column of white smoke rising from an oil distribution centre in Abha.

Confirmed images of the aftermath of the attacks in Saudi cities were not immediately available, and witnesses could not be reached in a country where media is tightly controlled.

The Houthis released pictures showing thick smoke and explosions of what they said were trucks from Saudi Arabia that they had hit in separate strikes at the border on Monday.

Houthi-controlled media reported later on Tuesday that Saudi war-planes had carried out four air-strikes in Yemen's Jubah district east of Sanaa.

Houthi spokesperson Yahya Saree accused Riyadh of having escalated the war by launching air strikes on Yemen, and said the Houthis would respond.

But Turki al-Malki, spokesperson for the Saudi-led coalition, said they "will take all necessary operational measures to deter this terrorist militia and resolutely confronts its hostile approach".

Tuesday's attacks hit Saudi oil facilities connected to an alternative route to the Strait of Hormuz, the Bab el-Mandeb, a strategic waterway off the southern tip of the Arabian Peninsula that connects the Red Sea to the Gulf of Aden.

The International Organization for Migration said more than 18,500 people had fled their homes because of fighting along Yemen's west coast over the past three days.

Global oil prices rise as fighting renews

Houthi attacks on south-western Saudi Arabia have the potential to worsen the war's global economic impact by disrupting Middle East energy supplies beyond the blockaded Strait of Hormuz.

These latest attacks, along with Iran and the US exchanging fire over the weekend, has sent global oil prices surging back towards the prices seen at the peak of the war.

Brent crude oil reached $US99.46 ($138) on Tuesday, the highest since mid-July, although the price eased a bit later in the day.

Washington is trying to increase the flow of oil to world markets by guiding ships through the Strait of Hormuz, while cutting off Iran's exports with a blockade.

Tehran has announced new measures to seal off the strait, saying it will soon unveil details of a "maritime exclusion zone" that will extend from the perimeter of the US blockade, through the strait and into the Gulf itself.

Reuters/AP