Question marks over global economic growth, and resulting oil demand, as well as over USA producers' capacity to pump oil at an ever faster pace make forecasting hard, the Organization of the Petroleum Exporting Countries said in its regular monthly oil market report. Most of that non-OPEC supply growth would come from the US, it said.
Oil prices ticked higher Thursday after data showed a decline in US petroleum inventories.
Nigeria's production plunged 150,000 b/d in the month to 1.73 million b/d, a one-year low, according to the survey by Platts.
Trump's tweet - similar to one he wrote in April, blaming OPEC for "artificially Very High" oil prices - came a week before a much-anticipated OPEC meeting in Vienna and may have been created to influence the discussion.
The two ministers agreed to expand cooperation in oil and gas, Russia's ministry said in a statement after their meeting in Moscow.
On Thursday morning, mixed comments from OPEC members cast further uncertainty over whether OPEC would maintain current production cuts or increase output over the course of the year, ahead of the June 22 OPEC meeting in Vienna.
U.S. oil benchmark West Texas Intermediate for July delivery finished up 28 cents at $66.64 a barrel on Wednesday, while European benchmark North Sea Brent oil gained $1.06 to $76.74 a barrel.
Outages due to the troubles in Nigeria and Venezuela's oil industries more than offset higher output from Saudi Arabia, Iraq and Algeria, the survey found, as May production fell 100,000 b/d from the previous month.
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Secretary of State Mike Pompeo, meanwhile, briefed his South Korean, Japanese and Chinese counterparts on the Singapore summit. Trump has also been widely criticized for his friendliness toward North Korean leader Kim Jong-un during and after the summit.
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"The deluge of United States crude production continues to hold the top-side in check", said Stephen Innes, head of trading at futures brokerage OANDA.
Demand for OPEC oil during the second half of the year is projected at 33.3 million barrels per day, down by about a half million barrels from the same period last year. A gallon of regular gasoline is now $2.91, up 25 percent from the year-ago level.
Oil prices steadied on Thursday, but were likely to remain under pressure from evidence of rising US output and uncertainty over the outlook for supply before a key meeting next week of the world's largest exporters.
"OPEC has the lowest spare capacity ever right now", said fund manager Pierre Andurand, in a tweeted response to Trump.
The president has been vocal about his dissatisfaction with oil prices in the past.
OPEC's actions, whether to cut or increase production, often heavily influence the price of oil, and by extension the prices consumers and businesses pay for fuel.
After peaking in May at $80.50 a barrel, prices have pulled back, with the price of Brent crude trading on Wednesday near $76 at barrel, partly in anticipation that the deal may end, and as Saudi Arabia and Russian Federation have already started increasing production. The ministers are gathering on June 20 as they debate an exit plan for the 2016 production cut deal, one of the key factors for pushing up oil prices.