Oil prices have edged higher in recent months, as the Trump administration has pushed allies to end all purchases of oil from Iran following the USA pulling out of the nuclear deal between Tehran and world powers, with ongoing unrest in Venezuela, as well as with fighting in Libya over control of that country's oil infrastructure.
The US ultimatum has also contributed to upward pressure on world oil prices, although Trump believes he has persuaded Saudi Arabia to offset this by ramping up its own production.
Along with OPEC+ curbing output by 1.8 Mbd, Venezuela's crude oil production continues to decline and could soon drop under 1 Mbd, depriving the market-and specifically USA refiners-of a major oil supplier.
The statement said the kingdom will coordinate with other producers.
After reducing production by more than 1.8 million barrels daily since January past year to drain a global glut, the producers decided in Vienna on June 23 to reverse course.
Iran is looking at ways to keep exporting oil as well as other measures to counter sanctions after the United States told allies to cut all imports of Iranian oil from November. Trump's tweet offered no timeframe for the additional 2 million barrels - whether that meant per day or per month.
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President Trump also touted the promise in a tweet Saturday.
Saudi Arabia's output is up 700,000 bpd from May, a Reuters survey found on Friday, and close to its 10.72 million bpd record from November 2016, more than making up for disruptions elsewhere within the Organization of the Petroleum Exporting Countries (OPEC). Keeping oil price around $70 per barrel serves both economic and political objective.
WTI (oil futures on NYMEX) witnessed good two-way price movements so far this Wednesday, now down more than a dollar from daily tops at $ 74.88, as the recovery attempts remain capped by the $ 74 handle.
Despite the apparent supply relief from Saudi Arabia, oil markets remain tense over escalating trade disputes between the United States and other major economies including China, the European Union, India and Canada, as well as the looming new U.S. sanctions against Iran.
The State Department has said it expects the "vast majority" of countries will comply with the US request.
US crude futures CLc1 were down 58 cents at $73.56 per barrel by 12:00 p.m. EDT (1600 GMT), still in sight of Tuesday's 3-1/2-year high above $75.
China, India, Japan, and South Korea are the top customers of Iranian crude.
An Indian official says his country, which imports 400,000 barrels per day of Iranian crude, would only recognise multi-lateral sanctions, rather than unilateral sanctions.