A number of countries have already cut reliance on Iranian oil, as well as other "traditional" sources of supply, due to surge in cheaper US crude exports.
"OPEC and particularly Saudi Arabia continue to drop not so quiet hints about the importance of higher oil prices - for the cartel and the upcoming IPO of Saudi Aramco", said Oil price.com, a prominent industry site.
The U.S. will cut its reliance on foreign oil to the lowest in more than 60 years as domestic crude output surges to record levels.
Expressing doubts over Iran's sincerity, Trump has threatened to walk away from the 2015 agreement by not extending sanctions waivers when they expire on May 12, which would likely result in a reduction of Iran's oil exports.
Suhail al-Mazrouei, UAE energy minister, also indicated OPEC would remain committed to its production cuts despite USA sanctions on Iran.
The EIA also boosted its price forecasts for both WTI and Brent for this year and next.
Exxon, which has been slow to capitalize on the shale revolution transforming the USA oil industry, has ridden the rise in oil prices to a 7% gain over the past month.
On Wednesday, a separate OPEC source had said Saudi Arabia was monitoring the impact of the US move on oil supplies and was ready to offset any shortage but would not act alone. Trump, a longtime critic of the 2015 deal, has said he'll withdraw the United States from it if other partners - mainly Britain, France, and Germany - don't "fix" its perceived flaws.
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A senior official with a Chinese oil major, who declined to be identified because he is not authorized to speak to the media, said new sanctions would hurt Chinese refiners by pushing up the price of crude.
Iran re-emerged as a major oil exporter in 2016 after global sanctions against it were lifted in return for curbs on Iran's nuclear program.
A day after Trump's decision, global benchmark Brent crude hit its highest since November 2014 at $77 a barrel on Wednesday on fears over tightening supply when inventories are shrinking due to production cut by Opec and Russian Federation since December 2016 and an uptick in demand. But, highlighting investor worries, the US -traded iShares MSCI Malaysia ETF plunged 6 percent overnight to a one-year low.
In other sectors, French carmaker PSA Peugeot Citroen agreed in 2016 to open a plant producing 200,000 vehicles annually in Iran, and says it is studying the implications of the USA move. It said it will comply with any sanctions. Firms would not be allowed to strike new deals with Iran.
"They're being disciplined", Kessens said.
Most of the companies should be able to withstand the loss of deals in Iran. This compares to last year's run rate at 95%.
Iranian missiles aren't aimed at Western Europe. Exports averaged 1.88 million barrels a day last week and have a cumulative daily average for the year of 1.64 million barrels a day, a 118% increase over the year-ago export total.
The EU purchased some 10 billion euros worth of goods from Iran in 2017.