The strikes overnight marked a fresh escalation in the widening Middle East crisis and came shortly after a coalition spokesman urged residents to evacuate the area for their safety.Â
Witnesses in Sana'a reported hearing explosions. It was not immediately clear which facilities were hit.
In a rare statement, the coalition urged civilians in the Houthi-controlled capital to leave the Yemeni Oil Company site and nearby storage areas ahead of a possible strike.
Houthi officials appeared to anticipate an attack on the site. The oil company said its storage facilities were empty and that a Saudi strike would not affect oil reserves or supplies for residents.
Shortly after the warning, Houthi military spokesman Brigadier General Yahya Saree said any Saudi attack on Sana'a would be met with a "firm and painful" response in Riyadh.
The area to be evacuated in western Sana'a, al-Subaha, is on a hill overlooking the capital. It is not a populated area, but the fuel station nearby is used by the public.
The back-and-forth threats come as Saudi Arabia is scrambling to determine how its air defences failed to intercept a barrage of missiles and drones fired by the Houthis, including an attack on Riyadh's international airport on Saturday that killed at least 13 people and wounded more than 300.
The latest conflict between the Saudis and the Houthis began in September after the rebels seized key areas along the Bab el-Mandeb Strait, a critical waterway for the transport of Gulf oil and other goods at the southern end of the Red Sea off Yemen.
The Saudi-led coalition, backing forces aligned with Yemen's internationally recognised government, has been trying to retake them.
Earlier on Tuesday, the Houthis renewed their warning against using Saudi airspace, Houthi-controlled media reported. Several airlines have suspended service to the kingdom because of the Houthi attacks on airports.
In a statement published by the Houthi-controlled SABA news agency, the Houthi-run foreign ministry referred to Saudi Arabia as the "Kingdom of the Horn of Satan" and said the kingdom "must realise that security, stability, and sovereignty must belong to everyone; otherwise, no one will enjoy them".
Meanwhile, Egyptian Foreign Minister Badr Abdelatty called for the Houthis to immediately halt attacks on Saudi Arabia.
"There is no justification for these attacks, and they cannot be accepted," Abdelatty told Iran's Foreign Minister Abbas Araghchi in a phone call Tuesday.
Abdelatty also called for prioritising diplomacy and a political solution to the conflict between Iran and the United States to avert "further escalation and instability" in the region, according to the Egyptian readout of the call.
The Saudi-led coalition said earlier on Tuesday that three drones were intercepted north of Riyadh. The Associated Press couldn't independently verify that claim.
Saudi Arabia has been pushing for the US military to provide more direct support in the fight against the Houthis.
The United States has provided intelligence sharing, target identification and planning for a Saudi-led offensive, but has held off on carrying out strikes against the Houthis.
A US intervention could prompt the Houthis to try to halt shipping through the Bab el-Mandeb, restricting the flow of oil out of the Persian Gulf.
President Donald Trump told reporters in Washington on Monday the Houthis were "misbehaving very badly," but didn't say anything about whether the US would respond to the rebels.
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