The official Saudi Press Agency confirmed a phone call between the two leaders about oil, but mentioned no specifics.
"Just spoke to King Salman of Saudi Arabia and explained to him that, because of the turmoil & dysfunction 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," Trump announced in an early morning tweet. "Prices too high! He has agreed!"
Later, the White House released a more cautious statement saying "the two leaders reaffirmed their dedication to a healthy and stable global energy market for the benefit of all nations."
"The two leaders agreed that balancing the global oil market is essential to ensure access to reliable and affordable energy to people everywhere," it said.
"In response to the president's assessment of a deficit in the oil market, King Salman affirmed that the kingdom maintains a two million barrel per day spare capacity, which it will prudently use if and when necessary to ensure market balance and stability, and in coordination with its producer partners, to respond to any eventuality."
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 1.5-2 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.