Major oil trading houses are predicting the return of $100 crude for the first time since 2014 as OPEC and its allies struggle to compensate for USA sanctions on Iran's exports.
Trump, whose decision to leave an global nuclear deal with Iran and reimpose sanctions on the country has pushed oil prices to levels not seen since 2014, on Thursday demanded that OPEC members lower the prices.
"Decisions can only be made at OPEC meetings in the presence of all OPEC members and by consensus of members", he noted.
"We protect the countries of the Middle East, they would not be safe for very long without us, and yet they continue to push for higher and higher oil prices!"
When Trump in May announced plans to reimpose sanctions on Iran's oil exports, the market estimated a cut of about 300,000 to 700,000 barrels a day, according to Trafigura's Luckock.
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But Mr Trump suggested on Twitter he will zero in on Iran, when he posted: "I will chair a United Nations Security Council meeting on Iran".
Higher gasoline prices for US consumers could create a political headache for Republican Trump before mid-term congressional elections in November.
"I don't know of any refiner in the world who is looking for oil and is not able to get it", Falih said, adding that Saudi Arabia could raise output by up to 1.5 million barrels per day (bpd) if needed.
Iranian Oil Minister Bijan Zanganeh said Trump's tweet "was the biggest insult to Washington's allies in the Middle East".
That equates to an increase of about 1 million bpd, but the latest figures show they are some way from achieving that target.
Such a price rally would mark the first time since the summer of 2014 that oil would return to the $100-a-barrel level that became the norm in the early part of this decade.
The Iranian oil minister warned that OPEC's authority is being jeopardized by the US shadow effect on the allies in the region. Brent crude has averaged year to date at $71 a barrel.