"Prices too high! He has agreed!"
The Saudi Press Agency said Trump had called Salman and the two highlighted "the necessity of doing efforts in order to preserve the stability of the oil market and the global economy growth."
They also discussed "efforts of the producing countries to cover any possible shortage in supplies," the agency said in its brief report.
Saudi Arabia is the world's biggest oil exporter and has usually kept at least 1.5 million to two million barrels per day of spare capacity, according to the United States Energy Information Administration.
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.
"This is just simply not doable," said one senior Saudi oil official cited by the Journal.
Trump has repeatedly lashed out at Opec on Twitter in recent months, piling pressure on Riyadh, a major ally, to boost output as he hopes for lower pump prices before midterm congressional elections in November.
His latest comments come a week after ministers from the Organization of the Petroleum Exporting Countries - of which Saudi Arabia is the major member - had agreed to raise output from July.
Non-Opec member Russia 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.
The ministers announced they would ramp up oil production by around one million barrels a day from July.
"I think it will contribute significantly to meet the extra demand that we see coming in the second half," Saudi Energy Minister Khalid al-Faleh told reporters at the time.
The talks had centered on whether to amend an 18-month-old supply-cut deal between Opec members and allied countries, including Russia, that has cleared a global oil glut and lifted crude prices.
The unprecedented supply-cut pact has lifted crude prices from below $30 a barrel in early 2016 to arouAFP.
Saudi Arabia, backed by non-member Russia, 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.
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 international nuclear deal with Tehran.
In the end, both sides were able to save face.
The current production curb pact calls for participating countries to trim output by 1.8 million barrels a day.
But production constraints and geopolitical factors have seen several nations exceed their restriction quotas, keeping about 2.8 million barrels off the market, according to Opec.
By agreeing to collectively raise output by a million barrels, member countries are simply committing to comply fully with the deal struck in late 2016.
Iran has accused Trump of trying to politicize Opec and said it was US sanctions on Iran and Venezuela that had helped push up prices. Saudi Arabia was producing around 10 million barrels of crude a day in May, according to Opec.