A little over an hour later, the Saudi Press Agency reported on the call but offered few details. "The two leaders stressed the need to make efforts to maintain the stability of oil markets, the growth of the global economy, and the efforts of producing countries to compensate for any potential shortage of supplies", Riyadh said in a statement.
At a meeting of the Organization of Petroleum Exporting Countries in Vienna, Saudi Arabia-the group's largest producer-joined other members in agreeing to scale back its over-compliance with output cuts that have been in place since the beginning of 2017.
The Democratic opposition has blamed part of that increase on Trump's decision to withdraw the U.S. from the 2015 nuclear deal with Iran, while Republicans fear that rising gasoline prices will boring Americans' enthusiasm for the USA economy as they approach next November's legislative elections.
There was no immediate comment from Saudi authorities.
Trump's warning last week about buying oil from Iran threw doubt and confusion into the energy market. "The two leaders agreed that balancing the global oil market is essential to ensure access to reliable and affordable energy to people everywhere", the White House said in a readout of the call.
Iran now exports around 2.4 million barrels a day of crude of which a million barrels or so could be at risk.
Saudi Arabia now produces some 10 million barrels of crude oil each day. The kingdom pumped slightly more than 10 million barrels a day in May.
"This is a situation where U.S. shale oil production itself has dropped in the past few months and that drop in the inventory has pushed oil prices up", Jordan said.
Trump was vague about whether the two-million-barrel increase would be per day.
Saudi Energy Minister Khalid al-Falih met with US Secretary of State Mike Pompeo in Washington on Thursday to discuss energy security.
Output is expected to rise to 11 million barrels in July, according to Reuters.
South Korea accounted for 14 percent of Iran's oil exports a year ago, according to the US Energy Department.
State Department officials said this week the United States is prepared to work with countries on a case-by-case basis to help them reduce imports of Iranian oil and suggested some exemptions were possible. Turkey stood at 9 percent and Italy at 7 percent.
FGE, an energy consultancy, said in its June newsletter that the U.S. is determined to "push Iran's exports to zero". Prices to high! He has agreed!
They will add to about 2.4 million barrels worth 16.81 billion yen ($153 million) imported in the year through May, according to the latest statistics from the country's Ministry of Finance.
Brent crude, the worldwide benchmark, was selling Friday for over $79 a barrel, and there is talk that in certain circumstances a return to $100 a barrel oil is possible.