Trump implied on Twitter that he had asked the king in a phone call to increase oil production in hopes of greater supply bringing costs down in the USA, which have risen since America stopped importing Iranian oil.
Saudi authorities had no immediate comment.
It was not immediately clear at what level of production Trump was referring to or by when.
Kuwait planned to raise oil output by 85,000 barrels per day starting on Sunday, part of an agreement between OPEC and non-OPEC producers to increase production by one million bpd, its Energy Minister Bakhit al-Rashidi said on Saturday. But he said it's unlikely that decrease could sustain itself as demand spikes, leading prices to rise by wintertime.More news: Suarez Says Rivalry With Ronaldo Different When Playing for Uruguay, Barcelona
In a morning tweet from his private Bedminster golf club, Trump said he made the request during a conversation with Salman, citing the "turmoil" and dysfunction in Venezuela and Iran for driving up prices at the pump.
"There is also some analysis from energy sector experts who say that Saudi Arabia could perhaps increase its daily output but it would only be for a very short time and the quality of the oil produced would be very low amd very hard to refine".
Im the run-up to the latest OPEC meeting, Riyadh, backed by Moscow, had argued strongly in favour of increasing production as grumbles in major consumer countries like the US, India and China have grown about higher prices.
Oil prices rose sharply in the spring as production collapsed in crisis-ridden Venezuela and traders anticipated Trump's withdrawal of the United States from the Iran nuclear deal. In the end, both sides were able to save face.
The world's top oil exporter plans to pump as much as 11 million barrels of oil per day (bpd) in July, an oil industry source told Reuters this week, after OPEC agreed with Russian Federation and other oil producers to raise output by about 1 million bpd.More news: Canada announces details of tariffs on USA goods
"We are moving into an environment where supply disruptions are visible all over the world, and of course President Trump has been pretty active in trying to isolate Iran and getting USA allies not to purchase oil from Iran", he added.
"If this trend, what the Russians and the Saudis have offered, I think it will lead to an implosion of the OPEC as an global trade institution", Cherkaoui added.
On Tuesday, a senior State Department official said the United States wants to stop all exports of Iranian oil from November and is unlikely to offer any exemptions as it did during previous sanctions. On Saturday, Iran's Supreme Leader Ayatollah Ali Khamenei accused the USA of being behind the unrest.
"If this happens, (it) means Trump is asking Saudi Arabia to walk (away) from OPEC", he told Reuters news agency.
'Saudi Arabia obviously can deliver as much as the market would need, but we're going to be respectful of the 1-million-barrel cap - and at the same time be respectful of allocating some of that to countries that deliver it, ' al-Falih said on Mpnday, prior to Trump's tweet.More news: Trump, at Rally, Vows to Carry On Anthony Kennedy's Legacy
"The market will go up to $100 I am sure as Saudi Arabia said they will plan an increase for July".