On Sunday, Opec and its allies at a meeting in Algiers ruled out any immediate boost in crude output but reassured the market that they would do whatever is necessary to balance the supply.
Mr Trump said last week that OPEC "must get prices down".
"The market does not have the supply response for a potential disappearance of 2 million barrels a day in the fourth quarter", Mercuria Energy Group Ltd.co-founder Daniel Jaeggi said in a speech at the S&P Global Platts Asia Pacific Petroleum Conference, knows as APPEC.
While Iran is unlikely to see a drop to zero exports, initial assessments by several analysts that about 500,000 barrels per day (bpd) of Iranian oil would be lost appear way too optimistic now.
Experts estimate that once U.S. sanctions on Iran are fully implemented from November it could result in the loss of as many as two million barrels a day from global supply. US light crude was $1.35 higher at $72.13.
Al-Falih added that Saudi Arabia, the cartel's largest producer, still expects to pump more crude in September and increase output again in October.
In August, OPEC and its allies cut production by 600,000 bpd more than their pact required, mainly as a result of falling output in Iran as customers in Europe and Asia reduced purchases ahead of the United States sanctions deadline.
As always, quantifying that cost is hard, but the co-head of oil trading at Trafigura, Ben Luckock, on Monday told the Asia Pacific Petroleum Conference, hosted by S&P Global Platts, that a price of $90 a barrel by Christmas and $100 by New Year was possible.
Sales of Iranian crude have fallen as buyers remain wary of penalties from sanctions due to take effect from November.
But he said producers would reduce "supply if there is ever. a demand shock to the market".
Iran's Ministry of Petroleum confirmed on Sunday that South Korea has halted oil imports from the Islamic republic. That suggests OPEC's power to influence the market will be tempered by USA production for about another decade. Earlier this month, the International Energy Agency warned there was a risk of oil prices spiralling higher in the coming months, posing a dilemma for the chancellor, Philip Hammond, as he looks to raise fuel duty. Money managers' wagers on higher Brent crude prices are having their longest streak since November 2017, according to ICE Futures Europe data.