The benchmark Brent crude on Thursday edged up on supply concerns, creeping closer to the psychological mark of $80 a barrel - a level not seen since November 2014.
On May 8, Trump announced he would pull the USA out of a 2015 pact - agreed by Britain, China, Germany, Russia and the Barack Obama administration - that opened up Tehran's atomic programme in return for an easing of sanctions.
Oil has risen 51% in the past year, driven by coordinated supply cuts and, this month, by concern over Iranian supply after the United States said it would reimpose sanctions on Tehran over its nuclear activities.
A senior official at Iran's state-owned oil supplier met Chinese buyers this week to ask them to maintain imports after USA sanctions kick in, three people familiar with the matter said, but failed to secure guarantees from the world's biggest consumer of Iranian oil.
Front-month Brent prices are now nearly $1.80 per barrel more expensive than those for delivery in December.
But before I get to Iran specifically, I want to remind you what has been happening in the oil market over the past year.
Traders say the surge in USA exports to more than 2 million bpd has saturated some markets, leaving benchmark prices ripe for a correction. Oil production in post-Arab Spring Libya is only 400,000 barrels per day, down from 1.6 million before the fall of Qaddafi.
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Now the bullish picture for oil is becoming more clear - isn't it? This was partly offset by record high domestic production, which restricted the decline below expectations.
Crude demand is now expected to increase by 1.4 million barrels per day, down from the previous prognosis of 1.5 million bpd, as a price rise of around 75% since last June to the current level of about $77 per barrel for Brent crude is expected to impact consumption. In early February, oil production broke through the 10 million barrels a day threshold for the first time in almost 50 years and has maintained the record levels thereafter. Since last September the price has increased from $50 to around $70 per barrel.
US shale oil production, meanwhile, is forecast to continue its climb.
However, stocks at the Cushing terminal in Oklahoma - the key delivery hub for USA crude futures traded on the New York Mercantile Exchange - edged up by 53,000 barrels to 37.2 million barrels.
Apart from supplies under annual contracts, CNPC and Sinopec have been lifting Iranian crude as part of their billions of dollars of investment at Iranian oil fields. In the year-ago period, the supply cover was 30.5 days. A stronger greenback makes it more expensive to buy dollar-denominated commodities like oil.
OPEC figures published on Monday showed oil inventories in OECD industrialized nations in March fell to 9 million barrels above the five-year average, from 340 million barrels above the average in January 2017.
"So there's really no need to adjust the production levels". Gasoline and distillate stocks were expected to have fallen by 2 million barrels and 1.3 million barrels, respectively.