This comes after the US Congress has reconsidered legislation aimed at preventing OPEC from manipulating oil prices.
Commodity traders Trafigura and Mercuria have also warned that Brent crude prices could rise to $90 per barrel by December and pass $100 in early 2019. Although he refrained from specifying how that could be done, Saudi Arabia is the only oil producer with significant spare capacity.
Benchmark Brent oil reached $80 a barrel this month, prompting Trump to reiterate on Thursday his demand that the Organization of the Petroleum Exporting Countries lower prices.
Oil investors are "trading the weekend news very favorably", said Stephen Innes, Singapore-based head of Asia Pacific trading with Oanda Corp.
Russian Energy Minister Alexander Novak said no immediate output increase was necessary, although he believed a trade war between China and the United States as well as USA sanctions on Iran were creating new challenges for oil markets.
An oil price spike is starting to look increasingly possible, with a rerun of 2008 not entirely out of the question, according to a new report. That was the highest level since November 12, 2014.
However, Saudi Arabia's influential oil minister Khalid al-Falih left the way open to a future production hike, as supplies tighten due to the USA imposing sanctions on Iranian oil from November this year.
He further said all producers - OPEC and non-OPEC - wanted to keep the price of oil at around $80 per barrel. They rose 0.3 per cent on Tuesday to close at their highest level since July 11.
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Seeking to reverse a downturn in oil prices that began in 2014, OPEC, Russia and other allies decided in late 2016 to reduce supply by some 1.8 million bpd.
Washington has already implemented financial sanctions against Iran and it plans to target the country's oil exports from November 4, putting pressure on other countries to also cut Iranian crude imports.
"We expect that those OPEC countries with available spare capacity, led by Saudi Arabia, will increase output but not completely offset the drop in Iranian barrels", said Edward Bell, commodity analyst at Emirates NBD bank.
Finger pointing and Trump-bashing came in the wake of the Organization of the Petroleum Exporting Countries (OPEC) deciding over the weekend to risk the wrath of volatile US president Donald Trump and not boost crude output, contrary to what many analysts and inside sources expected would happen.
Mercuria sees possibility of $100 spike in fourth quarter.
Oil markets have been driven up by looming US sanctions against Iran and an unwillingness or inability by Middle East dominated producer cartel OPEC and Russian Federation to raise output.
Saudi Arabia successfully negotiated limits on oil production 18 months ago in an effort to get oil prices higher and boost government coffers, which had suffered from an extended period of cheaper oil.