In the meantime, supply disruptions in Libya, Venezuela, and Canada, in addition to the larger-than-expected decrease in crude stocks in the USA, provided extra fuel to crude oil throughout the week.
"This will push the system close to the limit", and spare production capacity could fall below 2 million barrels a day - a level previously associated with $100 per barrel prices, the group said.
United States retail unleaded gasoline prices, including taxes, averaged $2.833 a gallon for the week ended 25 June, according to the nation's Energy Information Administration.
"We believe that Saudi Arabia will particularly increase output over the summer to meet its seasonally higher demand and bring Opec production to the target level".
Indian Oil Corp, Mangalore Refineries and Petrochemicals Ltd and Nayara Energy, the top three Indian buyers of Iranian oil, did not respond to Reuters's request for comments. The kingdom pumped slightly more than 10 million barrels a day in May.
"Supply deficit in the oil market is here to stay", Frank Schallenberger, head of commodity research at LBBW, said.
Trump tweeted of the meeting: "Hope OPEC will increase output substantially".
"Prices too high! He has agreed!"
OPEC and Russian Federation have said they will raise output to meet demand and replace crude from unplanned disruptions but many analysts think the extra supply may be inadequate.
Saudi Energy Minister Khalid al Falih met with US Secretary of State Mike Pompeo in Washington on Thursday to discuss energy security. It did not mention the two million barrel increase. A request by Trump for 2 million bpd more would be at least double market expectations.
Until then, however, Asia is buying as much Iranian oil as possible. Trump ordered the re-imposition of USA sanctions against Iran that were suspended under the accord. The US State Department announced it was aiming to drive the country's oil exports to "zero", rejecting the gradual approach to sanctions President Barack Obama's administration adopted back in 2012. Total's chief executive Patrick Pouyanne said last month that it was unthinkable for any global company to risk being excluded from the United States financial system - the penalty for buying Iranian crude beyond November 4.