A missile launched by Yemen's Houthi movement hit a building owned by Saudi Arabia's state oil company Aramco in the eastern city of Dhahran overnight, after a Saudi-led coalition struck a fuel depot near the Yemeni capital, Sanaa.

The Saudi energy ministry said the Houthi attack caused a "limited fire" in an administrative building at Aramco's headquarters complex.

Saudi authorities reported that several missiles and drones were intercepted elsewhere, and that falling debris injured four people in the capital, Riyadh.

The Houthis said they targeted Aramco and Riyadh's airport in response to the coalition's strike on the Yemen Petroleum Company's al-Sabaha facility on Tuesday.

The Iran-backed group also warned that there would be further attacks in the coming days.

International Monetary Fund director Kristalina Georgieva said the escalating conflict could have "potentially negative spillovers for everybody, everywhere".

The Saudi cabinet, chaired by Crown Prince Mohammed bin Salman, vowed on Tuesday that the Houthis would "bear the consequences" of their recent attacks on the kingdom, including a missile strike on Riyadh's airport on Saturday that killed 13 people.

The Houthis have said they are targeting airports, oil and gas facilities, and military bases in Saudi Arabia in retaliation for deadly Saudi air strikes on territory that they control in western Yemen, including Sanaa.

The Saudi-led coalition has been providing air support for Yemeni pro-government forces mounting an offensive against the Houthis on Yemen's Red Sea coast and other front lines.

On Tuesday evening, coalition spokesman Maj Gen Turki al-Maliki said its forces intercepted and destroyed a ballistic missile launched by the Houthis towards Dhahran, but that debris fell in a residential area.

Later, the Saudi energy ministry said an Aramco building in the city was targeted, causing a "limited fire" but no injuries.

Sources with knowledge of the incident told Reuters news agency that a ballistic missile hit an office tower in the company's headquarters complex, causing extensive damage and a fire that spread between the sixth and 10th floors. "[The] top three floors have gone," one Aramco employee was quoted as saying by AFP news agency.

Maliki said the coalition also intercepted missiles and drones launched towards Riyadh, al-Kharj and Haradh, as well as the country's south on Tuesday and Wednesday morning.

The General Directorate of Civil Defence said two women, a man and a child were injured by debris from two intercepted cruise missiles in Riyadh, which also caused "limited material damage" to 15 homes in the city.

The Houthis' military spokesman, Yahya Sarea, said on Wednesday morning that they had targeted Aramco's headquarters in Dhahran, an Aramco refinery in Riyadh and the capital's King Khalid International Airport with ballistic missiles, cruise missiles and drones.

"Operations towards Saudi depths will continue in the coming days, targeting Saudi enemy airports and oil facilities," he added.

The Houthis had threatened a "harsh and painful" response to the Saudi-led air strikes in Yemen on Tuesday afternoon.

Houthi-run media reported that the air strikes targeted the Yemen Petroleum Company's al-Sabaha Central Station, on the western outskirts of Sanaa, as well as its facilities at the Ras Isa oil terminal on the Red Sea coast, north of the port city of Hudaydah.

Two civilians were killed and two others were injured in the Ras Isa attack, the Houthi-run health ministry said.

The coalition had earlier issued a rare warning to civilians to evacuate the al-Sabaha fuel depot, saying it was planning a "special operation".

Queues reportedly formed at petrol stations in Sanaa following the warning, with many residents worried about shortages.

The Yemen Petroleum Company, which is run by the Houthis, issued a statement that sought to reassure them, saying the facility "does not contain any stock of petroleum products".

The company also said it had "taken all necessary precautionary measures to address any emergency, ensuring the stability of the supply situation and the continued meeting of citizens' needs in a normal manner".

Maliki said the coalition targeted al-Sabaha and other facilities because they were supporting Houthi "terrorist military operations".

"The militia has used these sites in their entirety to support its war effort by supplying its arsenal of missiles and [drones], which threaten the Kingdom of Saudi Arabia and the safety of airports, ports, and commercial vessels in the Red Sea," he added.

Houthi-run media also reported on Wednesday that a Saudi air strike in the south-western district of Shamayatayn killed a woman and that artillery fire killed two civilians in the north-western district of Shadaa, near the Saudi border.

Yemen has been devastated by a civil war that began in 2014, when the Houthis ousted the internationally-recognised government from Sanaa. The conflict escalated in 2015, after the Saudi-led coalition of Arab states intervened in an attempt to restore the government's rule.

A four-year-old informal ceasefire began to unravel in July, when the Houthis announced a "maritime embargo" against Saudi Arabia and began missile and drone attacks on Saudi airports, oil facilities and tankers in the Red Sea.

The Houthis said they were retaliating for what they call a Saudi blockade of their territory, as well as an air strike on Sanaa airport that they blamed on the kingdom.

The conflict escalated in September after the Houthis seized part of Yemen's south-western Red Sea coast near the Bab al-Mandab Strait, a chokepoint for global shipping. Their advance contributed to a rise in oil prices following six months of war between the US, Israel and Iran.

US President Donald Trump said on Truth Social on Tuesday the Houthis were "behaving very badly... and purposefully trying to drive up Oil Prices".

Speaking to reporters, he did not answer a question on whether he had made a decision to help the Saudis retaliate against them, but said he "might" ask Turkish President Tayyip Erdogan to intervene.

Last week, pro-government forces said they had regained control of territory overlooking Bab al-Mandab after launching a major counter-offensive with the support of Saudi air strikes.

Hundreds of people have reportedly been killed in Yemen since August. The UN's human rights office says they include at least 54 civilians, half of them children.

More than 216,000 people have also been displaced across the country, and suspected cholera cases have tripled in three weeks, rising from 217 to 647, according to the UN.