Prices rose on the data, with US crude futures up 53 cents to $61.93 per barrel as of 10:53 a.m. EDT.
"Based on such requests, Saudi oil production for the month of June is expected to remain below its OPEC+ commitment, while exports will also stay under 7 million barrels per day".
Iran President Hassan Rouhani says the country must counter USA sanctions by continuing to export oil as well as boosting non-oil exports.
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"The US government may possibly be preparing to put sanctions on Iran's petrochemical products because they know well that these products are one of the most important exports of Iran and bring significant foreign exchange to the country", he added.
India is scheduled to receive two crude carriers carrying 4 million barrels of Iranian oil this month. If Turkey decides to disregard US sanctions and continues to import oil from Iran, more troubling times could lie ahead for both Ankara-Washington ties and for the Turkish economy.
"The market is fearful that the other shoe is going to drop on the global economy if we get into a trade war; it will hurt oil demand", said Phil Flynn, an analyst at Price Futures Group in Chicago.
Most analysts expect Iran's crude exports to fall to little more than 500,000 bpd, down from around one million bpd in April, as governments largely bow to US pressure. The country is the world's largest oil importer. The deputy oil minister declined to provide recent oil sales figures for Iran but noted that Tehran would aggressively market its primary export, despite United States sanctions. -Chinese trade row, although persistent supply worries prevented a steeper price fall.