Chevron’s Chief Financial Officer Eimear Bonner told CNBC’s “Squawk Box” Europe show on Thursday that “it’s going to take time” for the prices Americans pay at the pump to fall, even as global oil prices drop sharply with tankers starting to move in greater numbers through the Strait of Hormuz.

“I mean there is a lag between oil prices and reduction in oil prices and when that shows up at the pump,” Bonner said.

Mr. Trump has criticized big energy firms and accused them of “gouging” American drivers by not cutting their prices, telling White House reporters Wednesday that he had ordered an investigation into the matter as “gasoline prices should be much lower at the pump.” 

The president singled out Chevron, ExxonMobil, Shell and BP by name.

70 ships transited the Strait of Hormuz on Wednesday, a 105% increase of traffic day on day, according to maritime business intelligence firm Kpler.

In a social media statement, the firm said ships were increasingly using a southern route through the strait that hugs Oman’s coastline, as opposed to one that brings them close to Iran’s coast in the north of the waterway.

Iran’s Islamic Revolutionary Guard Corps insisted Thursday that the only authorized route through the waterway is the one designated by Tehran, and it advised ships against using other routes.

Tanker movement has “risen sharply” in the Persian Gulf and the Gulf of Oman, which are linked by the Strait of Hormuz, since the U.S.-Iran deal was agreed last week, according to a maritime intelligence organization

“There’s been a material shift this week as tanker movements in the Middle Eastern Gulf have risen sharply since Iran and the U.S. agreed to reopen the strait,” Richard Mead, the Editor-in-Chief of Lloyd’s List said Thursday.

However, Mead said shipping firms were operating in a “limbo period” because it remains unclear what the circumstances in the Strait of Hormuz will be after the U.S.-Iran negotiations conclude, which is expected in less than two months under the memorandum of understanding signed by both nations.

“We don’t know what normal is going to look like yet,” Mead said

Iran and Oman have said they’re creating a new joint mechanism to control maritime traffic through the strait, as its coastal states, which could have “costs associated.” The Trump administration has said repeatedly that Iran will not be permitted under a final peace deal to charge ships fees or tolls, however.

Secretary of State Marco Rubio warned Thursday that allowing Iranian tolls on ships passing the Strait of Hormuz would create a precedent to other waterways, risking “total chaos.”

“International waterways do not belong to any nation state. This is a foundational principle in the world today, without which the world would be in total chaos,” he told a Gulf Cooperation Council meeting in Bahrain.

“If in fact we accepted that you can charge money to use an international waterway because it happens to be near your territorial space, well then this will spread throughout the world like a contagion.”

Rubio, on his first regional tour since the US and Iran signed a memorandum of understanding to end the Middle East war, said the US wants a peace deal but not “at any price”.

“While we want a deal, we don’t want a deal at any price,” he said. “We want a deal that’s good, we want a deal that’s real, we want a deal that’s verifiable, and we want a deal that’s adhered to.”

Brent crude, the international standard, fell 3.8% to $73.87 a barrel. It has been trading below $80 in recent days but is still above the roughly $70 per barrel it was trading at in late February before the war began.

U.S. crude prices fell 3.9% to $70.34 a barrel. Early Thursday, Brent was down 1.3% at $72.90, while U.S. benchmark crude lost 1.4% to $69.37.

The drop in prices comes as shipping across the Strait of Hormuz slowly resumed last week under the U.S.-Iran memorandum of understanding.

Secretary of State Marco Rubio was in Bahrain Thursday after promising Gulf allies that Washington would protect their interests as it seeks to hammer out a final settlement to end the war with Iran.

During a visit to Kuwait City, Rubio said Washington would be on the same page as Gulf states as it wrangles with Iran over a permanent settlement to the conflict.

“We’re going to be completely aligned with our partners in the Gulf,” he said, adding that the United States would “engage them on conversations about every decision that’s made with regards to this negotiation.”

Rubio is due to attend a Gulf Cooperation Council meeting in Bahrain on Thursday after sitting down with the leaders of Kuwait and the United Arab Emirates on Wednesday.

The initial US-Iran deal, which sets out a 60-day negotiating process aimed at reaching a long-term agreement, did not to address Gulf nations’ long-standing concerns about Iran’s missile program.

But Rubio insisted Washington was “not going to do anything that undermines the security of our allies”.

The Senate late Wednesday rejected a measure aimed at restricting President Trump’s power to wage war against Iran, in a victory for the president and Senate GOP leadership as they seek to quell congressional discontent with the Trump administration’s Iran strategy.

The procedural motion failed in a 50 to 47 vote, with two Republicans — Sens. Susan Collins and Lisa Murkowski — voting in favor of advancing the resolution by Democratic Sen. Tim Kaine, siding with most Democrats. Republican Sen. Rand Paul voted present, and Democratic Sen. John Fetterman voted no.

Just one day earlier, four Republicans voted yes on a separate House-passed resolution to restrict Mr. Trump’s war powers, allowing it to narrowly pass. Those same four GOP lawmakers had voted to advance the Kaine resolution in an earlier procedural vote last month — the first time an Iran war powers resolution had moved forward in the Senate after seven failed attempts.

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The Israeli military said Thursday that a soldier was killed the previous day in southern Lebanon, where clashes with Iran-backed Hezbollah have been reported despite a ceasefire.

Master Sergeant Basil Sweid, 32, a driver, “fell during operational activity,” the military said.

A spokesman told AFP he was killed when his vehicle overturned.

The military says 37 soldiers and one civilian contractor have been killed in southern Lebanon since fighting with Hezbollah erupted in early March.