Saudi state media reported that during the call, the Saudi king and Trump emphasized the need to preserve oil market stability and efforts of oil-producing countries to compensate for any potential shortage.
"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", SPA said. It did not elaborate.
Brent crude, the global oil benchmark, topped $80 per barrel in mid-May, the highest level since November 2014.
The White House statement undercut a tweet by Trump earlier in the day when he wrote that Saudi Arabia had definitely agreed to produce more oil.
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. Saudi Arabia has acknowledged that a call with Trump took place but mentioned no specific production targets.
Saudi Arabia, backed by non-member Russian Federation, had argued strongly in favor of increasing production as grumbles in major consumer countries like the United States, India and China have grown about higher prices.
But oil officials cited by The Wall Street Journal said it is debatable whether the kingdom would be able to raise output by the amount Trump suggested.More news: 7,000 crores of Indian money deposited in Swiss Banks in 2017
This comes after leaders from the Organization of the Petroleum Exporting Countries (OPEC) decided on increasing oil production by 1 million barrels per day, at a meeting last week. If so, such a boost would be significant for the country's oil production, which hit 10.03 million barrels per day (bpd) in May.
Saudi Energy Minister Khalid al-Falih met with U.S. Secretary of State Mike Pompeo in Washington on Thursday to discuss energy security.
US President Donald Trump and Saudi Arabia's King Salman attend a signing ceremony at the Saudi Royal Court in Riyadh.
"We will be in uncharted territory", Amrita Sen, chief oil analyst at Energy Aspects in London, said. Trump ordered the re-imposition of USA sanctions against Iran that were suspended under the accord. "While Saudi Arabia has the capacity in theory, it takes time and money to bring these barrels online, up to one year", said Amrita Sen of consultancy Energy Aspects.
Last week, OPEC led by Saudi Arabia and its allies including Russian Federation agreed to boost oil supplies after curbing output since 2017 to address a global supply glut.
The curbs were meant to help drain a global oil glut, a goal that has largely been achieved, though supply disruptions are now adding pressure to prices. The State Department is now insisting that other countries stop importing Iranian oil - or face sanctions from Washington.
Trump applauded the decision to increase supply, writing on Twitter that OPEC needs to "keep the prices down".
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.