Trump has given Britain, France and Germany a May 12 deadline to fix what he views as the flaws of the 2015 nuclear deal, or he will reimpose sanctions.
Crude has rallied this month amid heightened geopolitical tensions and Trump's indications that he might scrap the 2015 nuclear deal with Iran.
"That's an issue that is more political in nature that could have a shock in the market", said Mark Watkins, a regional investment manager at U.S. Bank Wealth Management in Park City, Utah".
Oil prices rose on Monday as Israeli Prime Minister Benjamin Netanyahu presented what he called evidence of a secret Iranian nuclear weapons programme.
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Looking at USA crude oil stocks, the most recent EIA figures (April 18) showed falling crude oil stocks and falling gasoline inventories.
A rise in U.S. government borrowing costs to their highest since 2013 this week has tempered some investor appetite for risk, but analysts said they believed Brent crude may have another attempt at marking new 2018 highs above $75 a barrel.
Netanyahu's disclosure of thousands of documents he said proved Iran definitively sought to assemble nuclear bombs comes as the US President, Donald Trump, considers whether to re-impose sanctions against Iran, the third biggest oil producer in the Organisation of Petroleum Exporting Countries.
West Texas Intermediate crude for June delivery traded at $67.44 a barrel on the New York Mercantile Exchange, down 66 cents, at 8:25 a.m.in New York.
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Brent was on track for a weekly gain of about 1 percent, while WTI was set for a weekly loss of about 0.3 percent. The global benchmark crude traded at a $6.43 premium to June WTI. The more-active July contract closed rose 90 cents to close at $74.69. At the same time, OPEC-led production cuts have continued to tighten global markets, despite record-setting United States crude output. Only Russia now produces more, at around 11 million bpd.
US crude inventories likely rose by 1.3 million barrels last week, while gasoline and distillate stockpiles fell, a preliminary Reuters poll showed on Monday ahead of data by the Industry group the American Petroleum Institute later in the day. US crude production rose by 46,000 BPD the previous week, to 10.59 MMBPD.
US drillers added five oil rigs in the week to April 27, bringing the total count to 825, the highest level since March 2015, General Electric's Baker Hughes energy services firm said.
Because of the tighter market, the forward curve for Brent is now above $70 per barrel until the end of 2018, and prices are above $60 per barrel through 2020.
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