U.S. West Texas Intermediate (WTI) crude futures CLc1 were at $72.22 a barrel, up 14 cents, or 0.2 percent from their last settlement.
For all these urgent supply pressures, the world's largest oil producers adopted a sit-back-and-wait approach at their meeting in the Algerian capital on Sunday. Now, the Saudis and OPEC want to institutionalise the new alliance.
Still, Trump has continued to take aim at OPEC for energy costs, demanding Thursday that the cartel "get prices down now!"
Ashley Kelty, oil analyst at financial services firm Cantor Fitzgerald said crude could soon hit US$90 per barrel. Analysts say that the Saudis are anxious about Trump's potential willingness to support such bipartisan legislation, which was rejected by Presidents George W Bush and Barack Obama.
Indian refiners - struggling from high crude feedstock prices and a sliding rupee - are planning to reduce oil imports in what could be a first sign that high prices are starting to hurt demand.
The bank forecasts Brent and USA benchmark WTI prices to average $85/Bbl and $76/Bbl, respectively, in the next six months.
"We have the consensus that we need to offset reductions and achieve 100 per cent compliance, which means we can produce significantly more than we are producing today if there is demand", Falih said.
The rise comes amid pledges by the Arabian Gulf Opec oil producers of sufficient oil production capacities to meet demand, even as the group remained vague about allotment of quotas during its latest technical committee meet on Sunday.
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OPEC and other oil producers are considering raising output by 500,000 bpd to counter falling supply from Iran. "As a result, the strength of oil prices is now putting oil demand growth at risk", he added.
Higher prices have helped to boost investment in crude globally, particularly in USA shale projects.
Portfolio managers have boosted their net position in Brent by 143 million barrels in the last four weeks, an increase of 44 percent, including by 51 million barrels in the two most recent weeks.
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After pulling out of the 2015 Iran nuclear deal in May 2018, the Trump administration has pledged to impose an embargo on Iranian oil from 5 November. In her view, the market does not focus enough on how Iran will react.
Also Sunday, OPEC released its World Oil Outlook 2040 report.
Commodity trading giant Vitol said on Tuesday that non-OPEC producers, especially the United States, may insert up to 2 million bpd of new crude into the market in 2019. However, analysts say that it is unlikely that the Kingdom will manage to bring this production to market quickly enough, and it will have difficulties in maintaining that level of production.
Opec and its allies reduced oil output in August as a drop in Iranian supply due to U.S. sanctions derailed their attempts to raise production to agreed levels, delegates said on Saturday as the energy producers prepared to hold talks in Algiers.