In a tweet on Saturday, Trump said the extra Saudi oil would help offset a decline in supply from Iran, after the United States pulled out of the Iran nuclear deal in May and moved to reimpose oil sanctions.
Iran had been pushing hard for oil producers to hold output steady as US sanctions are expected to hit its exports.
The Organization of the Petroleum Exporting Countries agreed with Russian Federation and other oil-producing allies on June 23 to raise output from July, with Saudi Arabia pledging a "measurable" supply boost, but giving no specific numbers.
USA officials are pressing allies in Europe, Asia and the Middle East to adhere to the sanctions once they are re-imposed, with the aim of pressuring Iran into negotiating a new agreement.
"Banking sanctions will also snap back on November 4, and we will be aggressively enforcing these provisions to lock up Iran's assets overseas and deny the Iranian regime access to its hard currency". "Prices to high! He has agreed!"
The president, in an interview with Fox News's "Sunday Morning Futures with Maria Bartiromo also piled pressure on close USA allies with a threat to sanction European companies that do business with Iran".
Norway-based Rystad Energy expects Iranian production to drop by 700,000 bpd by December 2018.
Looming U.S. sanctions against Iran further contribute to expected tightness.
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Unsurprisingly, Mr Trump's Twitter demands for increase in oil production and threats to OPEC "do not automatically create the pricing changes that he sought", said Ms Young.
After reducing production by more than 1.8 million barrels daily since January previous year to drain a global glut, the producers decided in Vienna on June 23 to reverse course.
Craig added that more issues could develop as Washington tightens the sanctions noose on Iran and Venezuela.
Oil production, prices and politics require a delicate balance.
Meanwhile, Libyan supplies are down by as much as 350,000-bpd after the closure of the country's two biggest ports, while Angolan production has also been falling due to chronic underinvestment. The facility produced 253,000 bpd on average previous year.
US President Donald Trump sent a message on Twitter that he asked Saudi Arabia to increase oil output by 2 million barrels because "prices to (sic) high".
Mr Trump took another swing at his European allies saying they dealt unfairly with the U.S. over trade.
"And so, we are not looking to grant licenses or waivers broadly on the reimposition of sanctions, because we believe pressure is critical to achieve our national security objectives", he said.