Trump's plans to impose sanctions on Iran, coupled with low production from Venezuela and blockades on some ports in Libya have continued to tighten global supply, pushing up oil prices.
Oil prices rose to multiyear highs last week after US officials signaled the administration would act to cut Iran exports faster than expected and.
Geoffrey Craig, the oil futures editor at Platts, said the drain on us inventory levels is in part because of higher domestic exports, which set a record for the week ending June 22 at 3 million barrels per day.
The official Saudi Press Agency confirmed a phone call between Trump and Salman about oil, but mentioned no specifics and the White House later struck a more cautious tone, saying in a statement the two leaders had "reaffirmed their dedication to a healthy and stable global energy market". "Of course. That's what we're doing, absolutely", he said.
But a flurry of United States announcements over the weekend unsettled oil markets.
"Such measures are taken as a psychological war against the country", Jahangiri made the remarks at a conference held to mark National Day of Industry and Mine in the capital Tehran.
This is while world oil prices have climbed higher as the Trump administration has pressured USA allies to end all purchases of oil from Iran.
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After the U.S. withdrew from the Iranian nuclear deal in May, it said it would reimpose economic sanctions against Tehran by November.
Also weighing on oil demand are trade disputes between the United States and other major economies including China, the European Union, India and Canada.
In a briefing with reporters, that official said Washington probably would not grant waivers from secondary sanctions against foreign companies that continue to do business with Iran.
He added, "We will prove that the USA claim to stop exportation of Iran's oil is an illusion". But those moves may be tempered by an equal desire by the U.S. and other country for stable oil prices.
Investors had questions as "to whether Saudi Arabia and Russian Federation could or would really be able to ramp production quickly enough", said Rob Haworth, who helps oversee US$151 billion at U.S. Bank Wealth Management in Seattle.
Iran and Saudi Arabia broke off diplomatic relations in 2016 and are locked in several proxy wars in the Middle East, including in Yemen.
Saudi Arabia has been pumping around 10 million bpd in recent months and sources close to its oil policy have said it could raise output to 11 million bpd.