Chevron's CEO said he was surprised that U.S. crude was trading below $73 a barrel because the “risks are very real.”
“A lot of the world's oil flows through this region, and if you were to cut it off, I think you could see that things would change very quickly,” Wirth said.
Chevron continues to transport crude oil through the region as the company works closely with the U.S. Navy's Fifth Fleet, Wirth said. The CEO warned that the situation is evolving.
“We really have to look very closely,” Wirth told CNBC.
British oil giant Shell has suspended shipments through the Red Sea, people familiar with the matter told the Wall Street Journal on Tuesday. Shell declined to comment when contacted by CNBC.
Shell's decision to halt deliveries across the crucial trade bottleneck comes about a month after BP halted Red Sea transits. Several major tanker companies carrying petroleum products such as gasoline and crude oil suspended traffic to the Red Sea on Friday.
Houthi fighters based in Yemen and allied with Iran have repeatedly attacked merchant ships in the Red Sea in response to Israel's war in Gaza. The US and Britain have launched airstrikes against Houthi targets in Yemen to secure shipping through the waterway.
The Houthis have continued to launch attacks despite US-led attacks. The militants fired an anti-ship ballistic missile on Tuesday that hit a Maltese-flagged bulk carrier in the Red Sea, according to U.S. Central Command. CENTCOM said no injuries were reported and the vessel continued to sail the waterway.
U.S. national security adviser Jake Sullivan said nations with influence in Iran need to take a stronger stance to show that “the whole world accepts the idea that a group like the Houthis can basically hijack the world like they did.” do it, completely rejects it”.
The UN Security Council passed a resolution last week condemning the Houthi attacks “in the strongest possible terms”. Permanent Council members China and Russia, which have veto power, abstained from voting on the resolution.
“We anticipated that the Houthis would continue to attempt to keep this vital artery at risk, and we continue to reserve the right to take further action, but this must be an all-out effort,” Sullivan said during one Interviews in Davos on Tuesday.
Oil market and geopolitical analysts say the biggest risk to energy supplies would be if tensions in the Middle East lead to a regional conflict that disrupts crude flows from the Strait of Hormuz.
About 7 million barrels of crude oil and crude oil products pass through the Red Sea daily, compared with 18 million barrels that pass through the Strait of Hormuz, according to data from trade analysis firm Kpler.
Goldman Sachs has warned that a prolonged disruption in the Strait of Hormuz could double oil prices, although the investment bank believes that scenario is unlikely.
Wirth said Chevron had two ships attacked by the Iranian Navy last year, one of which was hijacked by commandos and taken to an Iranian port and the other came under fire for four hours until the U.S. Navy intervened.
Iran seized an oil tanker in the Gulf of Oman last week. The Marshall Islands-flagged tanker St. Nikolas was previously embroiled in a dispute between the U.S. and Iran over sanctioned crude oil.