Saudi Arabia plays a critical role in the oil cartel.
The kingdom is the world's top oil exporter and the leader of the oil-producing bloc.
USA officials acknowledged the call at the time, but offered no details.
Trump has pressured OPEC to lower crude oil prices as the cost recently increased above $80 per for Brent. If the White House was informed about the secret private deal, it didn't seem to resolve Trump's concerns. "Not good. We want them to stop raising prices, we want them to start lowering prices", Trump said at the United Nations General Assembly.
Also, the secrecy behind the private deal is interesting. Was that a deliberate strategy by the Saudis to leak the details to the press in order to inform the market?
Brent on Wednesday hit a four-year high of $86.74 a barrel.
Saudi energy minister Khalid al-Falih said the country had raised output to 10.7m barrels per day in October and announced a further production hike in November.
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Meanwhile, U.S. crude oil production C-OUT-T-EIA remained at a record-high of 11.1 million barrels per day (bpd).
"Mr Trump is very angry with some countries for not being able to replace the Iranian oil and has expressed this anger in his remarks to the Saudi king and to OPEC for not increasing output", he said.
Criticizing America's longstanding military relationships with allies has been a hallmark of Mr. Trump's presidential campaign and his time in office.
Qatar hosts the largest USA military base in the region. But I said 'King - we're protecting you - you might not be there for two weeks without us - you have to pay for your military, ' said Trump at a rally in Southaven, Mississippi, on Tuesday.
US weekly Midwest refinery utilization rates dropped to 78.9 percent, their lowest since October 2015, according to the data.
Trump has yet to demand payment for keeping U.S. troops in the oil-rich region, but the USA president did urge them to lower oil prices in return for security last week.
Saudi Arabia and Russian Federation have increased production as a result but last month Opec and non-Opec members ruled out a further hike to compensate for the expected 2m barrel a day loss from Iran. "OPEC is not trying to manipulate the price, it's trying to bring the market to balance", he told CNBC.