Along with the rise in non-OPEC production, the agency sees demand growth of 1.4 million barrels a day, down by 100,000 barrels from last month's report.
Prices have risen since President Donald Trump decided last week to pull the USA out of the Iranian nuclear deal, meaning that sanctions will be re-imposed on the oil producer that are likely to impact its production and push prices higher.
At 432.4 million barrels, US crude oil inventories are in the lower half of the average range for this time of year.
Crude oil prices are now flat - both Brent and WTI are trading sideways today. As for Opec, leading members have assured traders they have plenty of crude to make up for any losses from sanctioned Iran, though the oil cartel showed no signs of ramping up output.
If the political prospects improve in countries like Venezuela, Libya, South Sudan, and Iran, prices will fall even lower.
But Money Morning Global Energy Strategist Dr. Kent Moors sees even more reasons that the oil market will continue to feel the pressure, not the least of which are OPEC production problems in Venezuela, Nigeria, and Libya.
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As a result of its surging production, USA crude is increasingly appearing on global markets as exports.
The prospects of a sharp drop in Iranian oil exports in the coming months due to renewed U.S. sanctions following President Donald Trump's decision to withdraw from an worldwide nuclear deal with Tehran has lifted oil prices in recent weeks.
China is crucial to global oil demand growth, and if it keeps its current growth pace, it would support the strong demand growth that analysts expect. The price of WTI crude, meanwhile, hit $72.10 per barrel.
This trend in the global oil market could force the Narendra Modi government to roll-back excise duty on petrol, diesel, which remains staggeringly high.
Markets have been reacting to the prospect of a sharp drop in Iranian oil exports after the USA decision on the deal. The compliance rate for the 10 non-OPEC nations participating in production cuts fell to 73 percent in April versus a revised 79 percent in March, according to Bloomberg calculations from preliminary IEA data on crude output.
Despite Wednesday's dips and some indicators implying the financial oil has overshot physical oil, overall crude market conditions have tightened since 2017 when the Organization of the Petroleum Exporting Countries (OPEC) started to withhold supplies to push up oil prices.
OPEC and its ally Russian Federation have cut their output since January 2017 to help reduce excessive global stockpiles.