In response, a senior Iranian official accused Mr Trump of sending prices even higher through his tweets.
A survey of analyst expectations from S&P Global Platts revealed expectations of a drain on US crude oil inventories of 4.5 million barrels last week, adding support to the concerns about a market deficit.
The United States pulled out of a multinational deal in May to lift sanctions against Iran in return for curbs to its nuclear programme.
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U.S. West Texas Intermediate (WTI) crude futures CLc1 were at $74.60 a barrel at 0044 GMT, up 46 cents, or 0.6 percent, from their last settlement.
Antoine Halff, formerly a chief oil market analyst at the International Energy Agency and now senior fellow at Columbia University, said that Trump made three errors in his tweet: OPEC can influence market prices but is not a monopoly. "OPEC has not defined oil prices for the past 30 years, it is a financial market and regional hubs for marker crudes who does it?"
Trump's plan is to get the Gulf countries to commit to increase output by over two million barrels per day to offset falling supplies elsewhere.
In a tweet on Saturday, Mr Trump said Saudi Arabia had agreed to increase oil output by up to two million barrels.
Brent crude declined from its $115 per barrel peak in June 2014 to below $30 in January 2016 before recovering to its current price of around $78.
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Iran's OPEC governor Hossein Kazempour Ardebili said the United States ban amounted to "self harm", adding that Iran's position is that oil should not be used as a weapon or for political purposes. Analysts and traders were predicting a draw of 1 million barrels.
Iran's OPEC governor Hossein Kazempour Ardebili speaks to journalists at a news conference in Tehran, Iran March 7, 2005.
This time around, the US sanctions and the tough USA approach to try to cut off as many Iranian oil barrels as possible have spooked banks, insurers, and shippers, who have started to wind down business with Iran for fear of coming under secondary sanctions.
The head of Iran's Revolutionary Guards said on Thursday their forces were ready to implement Iran's threat to block the Strait of Hormuz and that if Iran can not sell its oil under the US pressure, no other regional country will be allowed to.
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The official said that the "responsibility is beyond any one technology company" and "requires partners", according to the paper. Similarly, the app also introduced a feature which allows group administrators to decide who gets to send messages in a group.