Supply to the US market has also been squeezed by the loss of some Canadian oil production.
"Rising production from Middle East Gulf countries and Russian Federation, welcome though it is, comes at the expense of the world's spare capacity cushion, which might be stretched to the limit", the Paris-based agency said in its monthly report. "This vulnerability now underpins oil prices and seems likely to continue doing so".
President Trump has been pressuring the Organization of the Petroleum Exporting Countries, or OPEC, to increase production to cool off oil prices, which recently hit the highest levels in over three years.
"Higher prices are prolonging the fears of consumers everywhere that their economies will be damaged".
Venezuela's total output capacity could sink below 1 million barrels a day by the end of the year, bringing its overall loss in 2018 to more than 40 percent, the IEA said.
China and India, the world's second and third largest oil consumers, could face "major challenges" in finding alternative crude oil following the drop in Iranian and Venezuelan exports, the IEA said.
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Saudi Arabia said that it pumped almost 10.5 million barrels per day last month, compared with 10 million in May. They can increase investment in USA production, raising employment in extraction and raising demand for oil drilling equipment.
Reports show that production fell to 527,000 barrels per day (bpd) from a high of 1.28 million bpd in February following the port closures.
And while Iran has yet to feel the full impact of renewed United States sanctions, the IEA fears there could be "an even steeper reduction than the 1.2 million barrels per day seen during the previous round of sanctions".
The agency, which oversees the release of emergency oil stockpiles held by importing nations, reiterated that it's monitoring developments in case any action is required.
Crude oil prices also fell as the USA dollar rose on Wednesday's surprisingly strong US inflation report, which increased prospects the Federal Reserve will raise interest rates twice more this year. Fuel costs have sparked protests in Brazil and Russian Federation, and complaints from India. "If these tariffs are introduced, there will be an impact on global growth and demand".