There was no immediate comment from Saudi authorities.
Non-OPEC member Russian Federation on June 23 also backed the effort, capping a week of tense diplomacy for the bloc that averted a damaging rift between arch foes Iran and Saudi Arabia.
It was not immediately clear at what level of production Trump was referring to or by when.
Fundamentally, global Brent crude oil remains firm because looming sanctions by the White House against Iran are expected to lead to a sharp drop in supplies from the OPEC-member.
"This is a situation where USA shale oil production itself has dropped in the past few months and that drop in the inventory has pushed oil prices up", Jordan said.
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 decision follows a meeting of oil ministers from around the globe at the Organization of the Petroleum Exporting Countries (OPEC) in Vienna, where they decided on a production increase in order to keep prices low.
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Investors are betting Saudi Arabia has little room to respond to a future crisis should it boost output even more to meet Trump's request, as Saudi Arabia only has about 2 million barrels of unused capacity, according to International Energy Agency. In the end, both sides were able to save face.
Besides the looming USA sanctions against Iran, which is fueling the rally in Brent futures, and the outage in Canada, which is supporting WTI crude, both markets are also benefitting from supply issues in Venezuela and Libya.
"He has agreed!" Trump tweeted.
"If this trend, what the Russians and the Saudis have offered, I think it will lead to an implosion of the OPEC as an worldwide trade institution", Cherkaoui added.
"They bring to bear economic pressure to separate the nation from the system ... but six USA presidents before him tried this and had to give up", Khamenei was quoted as saying on Saturday by his website Khamenei.ir, referring to Trump.
Over the past six months, Iran's currency has lost nearly 50 percent of its value, with the USA dollar now buying around 85,000 rials on the open market.
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. "If they do, it means the State Department is running OPEC".
"The market will go up to $100 I am sure as Saudi Arabia said they will plan an increase for July".