The statement reported by Saudi media did not mention any intention by Saudi Arabia, the world's top oil exporter, to raise production to 2 million barrels per day.
"During the call, the two leaders stressed the need to make efforts to maintain the stability of oil markets and the growth of the global economy", the statement said. It did not elaborate.
"Just spoke to King Salman of Saudi Arabia and explained to him that, because of the turmoil & disfunction [sic] in Iran and Venezuela, I am asking that Saudi Arabia increase oil production, maybe up to 2,000,000 barrels, to make up the difference", the United States president wrote on Twitter on Saturday. "He has agreed!", Mr Trump said on Twitter Saturday.
Rising oil prices are impacting American prices at the pump.
"Prices too high! He has agreed!"
An agreement by an OPEC member nation to increase oil output at the request of a US president would be a serious blow to that alliance of 15 oil-producing countries, which sets production quotas collectively, and has already shown fragility in recent days.
"It is becoming increasingly clear that Saudi Arabia and Russian Federation will struggle to compensate for potential losses in oil production from the likes of Venezuela, Iran and Libya", said Abhishek Kumar, analyst at Interfax Energy in London. Saudi Arabia would like oil prices to remain elevated, while appeasing President Trump.
Continuing increases came despite the decision last week by OPEC and its allies to increase production by as much as 1 million barrels per day.
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Saudi Arabia now produces some 10 million barrels of crude oil each day.
Saudi Energy Minister Khalid al-Falih met with U.S. Secretary of State Mike Pompeo in Washington on Thursday to discuss energy security.
The US president says King Salman agreed, although that claim remains unconfirmed by Riyadh.
"We will be in uncharted territory", Amrita Sen, chief oil analyst at Energy Aspects in London, said. Iran has accused Trump of trying to politicize OPEC and said it was USA sanctions on Iran and Venezuela that helped push up prices. "While Saudi Arabia has the capacity in theory, it takes time and money to bring these barrels online, up to one year", she said.
Non-OPEC Russia, meanwhile, was under pressure from its own energy companies to lift caps on output and fight a steep rise in domestic fuel prices that was hurting President Vladimir Putin's popularity, Russian sources have said.
It was not immediately clear at what level of production Trump was referring to or by when.
Oil prices have edged higher as the Trump administration has pushed allies to end all purchases of oil from Iran following the US pulling out of the nuclear deal between Tehran and world powers. "Triple-digit oil prices are not off the table", JBC said. The State Department is now insisting that other countries stop importing Iranian oil - or face sanctions from Washington.
That's up about 55 cents from the same period a year ago, at a time Mr Trump's Republican Party is trying to hold on to its majorities in Congress in the November midterm elections.
Non-OPEC member Russian Federation on June 23 also backed the effort, capping a week of tense diplomacy for the grouping that averted a damaging rift between arch foes Iran and Saudi Arabia.