However, the U.S. Energy Information Administration estimated that OPEC crude production only decreased from 32.7 million barrels per day in 2016 to 32.5 million in 2017, a drop of less than one per cent.
White House said, the two leaders reaffirmed their dedication to a healthy and stable global energy market for the benefit of all nations.
Trump's tweet offered no context for the supposedly promised additional 2 million barrels of crude oil to be produced by Saudi Arabia, so it's not clear whether that was intended to mean per day, or something else.
It was not clear if Trump meant an extra two million a day, but analysts speaking to Bloomberg News believe the kingdom can produce more than 12 million a day - which would leave an nearly two-million barrel gap per day.
Iran opposed any changes to the original production-cut deal at a time when its oil industry is facing renewed sanctions over Trump's decision to quit the global nuclear deal with Tehran.
On Saturday, Iranian Supreme Leader Ayatollah Ali Khamenei said the USA was trying to drive a wedge between Iranians and their government using "economic pressure".
The Democratic opposition has blamed part of that increase on Trump's decision to withdraw the USA from the 2015 nuclear deal with Iran, while Republicans fear that rising gasoline prices will tiresome Americans' enthusiasm for the United States economy as they approach next November's legislative elections.
The administration has threatened close allies such as South Korea with sanctions if they don't cut off Iranian imports by early November.
In addition, mid-term elections are due in the USA in November. The continued political crisis in Venezuela has also contributed to the price increase.
It added that there also was an understanding that oil-producing countries would need "to compensate for any potential shortage of supplies".
In a meeting between Russian Federation and OPEC earlier this month, Saudi Arabia and Moscow helped to convince the cartel's members to raise production as countries such as the US, India and China - the major consumers of oil - complain about high prices.
Trump in May withdrew the United States from a 2015 agreement that curbed Tehran's nuclear capabilities and ordered the reimposition of USA sanctions against Tehran. In the end, both sides were able to save face. The Saudi leader said he was ready to raise output if needed, the White House said in a statement.
There was no initial comment from the Saudi authorities.
"If this trend, what the Russians and the Saudis have offered, I think it will lead to an implosion of the OPEC as an global trade institution", Cherkaoui added.
"Six US presidents before him tried this and had to give up", Mr Khamenei cautioned on his website.
In Libya, the supply of up to 780,000 barrels of crude a day is at risk, according to analysts. venezuela's sliding output is also helping boost prices as the U.S. sanctions that country.