Oil hesitated at the start of the week, but traders are coming back to the buy side of the table as markets realized Saudi Arabia is in no rush to push oil prices higher again after recently pushing OPEC to lift production limits just last month.
Information provider Genscape said USA crude inventories at the Cushing, Oklahoma, delivery hub had fallen in the week, traders said.
Mr Trump's interventions with tweets "unsettle" the market and appear to have pushed prices up, Standard Chartered Plc energy analyst Emily Ashford and head of commodities research Paul Horsnell wrote in a note Tuesday.
USA crude inventories fell by 4.5 million barrels in the week to June 29 to 416.9 million barrels, according to the American Petroleum Institute (API) on Tuesday.
Iran's President Hassan Rouhani on Tuesday said it was "unwise to imagine that some day all producer countries will be able to export their surplus oil and Iran will not be able to export its oil".
Trump was not specific on whether the additional 2 million barrels was a per-day figure - but worldwide daily demand is nearing 100 million bpd. "On balance, this leaves the oil market tighter than before, with less spare capacity".
At the same time, the official said, the United States would work with countries that import Iranian crude on a "case by case" basis, signaling that the Trump administration might not immediately impose sanctions on those that continue importing from Iran beyond a November 4 deadline. "And yes, we will certainly be requesting that their oil imports go to zero, without question".
US crude futures CLc1 were up 19 cents at $74.33 a barrel, within sight of Tuesday's 3-1/2-year high above $75 a barrel.
Russian Federation and Saudi Arabia will face "dire consequences" if they increase their oil production, the head of the state energy firm said.
Oil sanctions on Iran are expected to resume on November 4, two days ahead of congressional midterms.
Craig added that more issues could develop as Washington tightens the sanctions noose on Iran and Venezuela. Global benchmark Brent fell 2.4 percent in the session, changing direction from last week when it gained more than 5 percent.
Saudi Arabia's King Salman promised U.S. President Donald Trump at the weekend that he would raise oil production if needed and the country has 2 million barrels per day of spare capacity to boost output, the White House said.
"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.
Mr Trump is not the first US President to attack OPEC.