Iranian oil exports have increased by roughly 1 million barrels per day since early 2016, and the big question is whether the market will be able to cope with a sharp drop in supply if sanctions are reimposed.
Looking at reactions in markets, crude oil prices weakened immediately following the EIA report.
Trump telegraphed the move, and oil prices shot up in recent weeks as traders anticipated it.
With global supply already on a downward slope, Iran sanctions could be the last straw to shift the market dynamic, said Leigh Goehring of Goehring & Rozencwajg Associates.
In other data, the United States rig count increased by nine to a total of 834 producing oil rigs.
The U.S. crude price broke above $70 a barrel today, and Brent crude, the global oil benchmark, hit $75.59 a barrel - the highest level, in both cases, since 2014.
This, in addition to the ongoing tensions in Venezuela lifted WTI crude oil to above $70.
Trump leaving the deal could undermine a 2015 agreement supported by allies of the United States in Europe, as well as Russian Federation and China.
"I am announcing today that the USA will withdraw from the Iran nuclear deal", Trump said.
"The kingdom will work with major producers and consumers within and outside OPEC to mitigate the effects of any supply shortages", the state-run Saudi news agency reported, citing a statement issued by an official in the energy ministry.
An increase in oil production leads to lower prices.
Oil market analysts argue that restoring sanctions will be less disruptive than in 2012-15, estimating that exports would fall by 300,000 to 500,000 b/d.
The United States now produces more crude oil than top exporter Saudi Arabia, and two weeks of U.S. inventory builds have limited the oil market's upside.
Given that this is an election year, the Centre could have blinked first to temper oil prices. Gasoline inventories declined by about 2.1 million barrels, and distillate stockpiles decreased by 6.7 million barrels.
That's because the European Union, whose members have been urging Trump not to pull out of the deal, may not go along with new sanctions.
Iran said that its uranium enrichment activities are strictly for energy generation.
Total products supplied over the last four-week period averaged about 20.3 million barrels per day, up by 2.7 percent from the same period past year.
The British central bank had until recently been expected by investors to hike rates this month.
Saudi Arabia, for instance, has the ability to crank up output.
Other major producers could fill the hole left by Iran.