Traders assessing the impact of the US withdrawing from the Iran deal, combined with issues in Venezuela and a strong USA inventory report has led prices to rise, said Craig Bethune, a senior portfolio manager at Manulife Asset Management.
Mr Trump said the nuclear agreement was a "horrible, one-sided deal" that "didn't bring peace" and "never will".
The Treasury imposed the sanctions on nine Iranians and companies it said were operating a corrupt currency exchange network in the United Arab Emirates with complicity from Iran's Central Bank.
Crude surged past $71 for the first time since 2014 as American stockpiles shrank and the USA told crude buyers to curb purchases from Iran.
Directly and indirectly, these sanctions will impact on those who deal in Iranian oil, insure Iranian crude oil cargoes, underwrite tankers in Iranian waters, and on the National Iranian Tanker Company (NITC).
The rise came in the aftermath of US President Trump's decision to abandon a nuclear deal with Iran and his announcing the "highest level" of sanctions against Iran, a member of the Organisation of the Petroleum Exporting Countries (OPEC). With President Donald Trump's decision to reimpose sanctions on Iran driving up oil prices, shale's less-loved plays are starting to look a bit more promising.
The United States plans to impose new sanctions against Iran, which produces about 4 percent of global oil supplies, after abandoning an agreement reached in late 2015 that curbed Tehran's nuclear activities in exchange for removal of US and European sanctions.
"There are few issues more important to the security of the U.S. than the potential spread of nuclear weapons or the potential for even more destructive war in the Middle East".
Additionally, OFAC is revoking its favorable licensing policy applicable to USA persons for civil aircraft and parts, and US imports of Iranian carpets and foodstuff once again will be restricted.
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The global oil market is balanced, with top exporter Saudi Arabia and No.1 producer Russian Federation having led efforts to curb oil supply to prop up prices. Unless the European signatories to the deal and the US Congress addressed his concerns, he plans to withdraw on the next deadline for waiving sanctions.
The Organization of the Petroleum Exporting Countries has a deal with Russian Federation and non-OPEC producers to cut supplies that has helped erase a global glut and boosted oil prices to their highest since 2014.
USA investment bank Jefferies said in a note it expects Iranian crude oil exports to start falling in the next few months. Effective November 5, 2018, General License H - which authorized non-U.S. entities owned or controlled by USA persons to engage in certain activities with Iran - will be terminated, after which point such activities will be prohibited.
Setting fire to a paper US flag and chanting "Death to America", the lawmakers symbolized the anger felt by many Iranians as Trump reneged on the Obama-era deal, signed in 2015 after two years of intense negotiations.
Even without disruption to Iran's crude flows, the balance between supply and demand in the oil market has been tightening steadily, especially in Asia, with top exporter Saudi Arabia and No.1 producer Russian Federation having led efforts since 2017 to cap output to prop up prices.
Outside OPEC, soaring US crude oil production could help to fill Iran's supply gap.
Crude oil traded slightly bearish during the Asian session in response to the ruthless rise in USA drilling activity pointed to increased output.
At the end of May, le Maire will meet British and German finance ministers to also look at "what we can do in response to these USA decisions on extraterritoriality", the minister said, adding that "It is urgent to go from words to deeds".
May reaffirmed Britain's support for the deal alongside France, Germany and the European Union, insisting it was "the best way of preventing Iran from developing a nuclear weapon", according to a readout of the phone call.