Trump wrote on Twitter that he had asked the king in a phone call to boost oil production "to make up the difference..." The Saudi leader said he was ready to raise output if needed, the White House said in a statement.
In this scenario, Saudi Arabia, the UAE, Kuwait and Iraq are the main countries that have the capacity to increase production, she said. "It is expensive", a Saudi official told the paper.
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. The International Energy Agency, the Paris-based group that represents consumer countries, recently estimated what it called "short order supply" from the Middle East, including Saudi Arabia, at 1.14 million barrels a day.
"Because of (sanctions on) Iranian crude, we are looking at USA heavy crude" as a substitute, the source said, in particular grades such as Southern Green Canyon and Mars, which are similar to crude from Iran.
Price increases have also been driven by Trump's decision to withdraw from the Iran nuclear deal and reimpose trade sanctions there. North America's oil markets have tightened significantly this week as an outage of Canada's Syncrude has locked in over 300,000 bpd of production.
"If we take 2 million barrels of oil off the market, what is going to be left in the tank?"
Pressure from Tump did help prod Saudi Arabia, Russia and other producers to agree to gradually increase supply by as much as 1 million barrels a day at meetings on June 22 and June 23 in Vienna.
"If the Saudis were really to raise output by 2 million barrels a day, their maximum capacity according to the International Energy Agency, that may backfire from an oil price standpoint by leaving the oil market with no meaningful spare capacity to handle any possible future supply problems, from geopolitics in places like Iran or Libya to hurricane season to any other issues", said Jason Bordoff, director of the center for global energy at Columbia University.
"We will be in uncharted territory", Amrita Sen, chief oil analyst at Energy Aspects Ltd.in London, said.
Iran's Supreme Leader Ayatollah Ali Khamenei on Saturday accused Washington of trying to turn Iranians against their government.
"They bring to bear economic pressure to separate the nation from the system. but six U.S. presidents before him tried this and had to give up", Khamenei was quoted as saying on Saturday by his website, referring to Trump.
"The market will go up to $100 I am sure as Saudi Arabia said they will plan an increase for July. This was managed between the two to rob the pocket of rest of the world", he said.
Khalid al-Falih the Saudi Energy Minister, told CNN's John Defterios in an interview at the latest OPEC meeting that the demands by major consuming nations would be met, but he didn't expect the kingdom to add 2 million more barrels a day.