Still, oil prices could also come under downward pressure from an economic slowdown.
The U.S. bank said January global crude oil demand growth was "nearly 2.0 million barrels per day, with strength visible in both emerging markets and developed economies".
Production is expected to increase 1.35 million bpd compared to the previous year, but will grow more slowly than the previous forecast of 1.45 million bpd.
Oil prices have risen since the beginning of this year thanks to supply cuts led by OPEC.
Another influence for traders was US sanctions against oil exports from Iran and Venezuela said to be contributing to the tightening: Barclays noted that "Failures in [Venezuela's] electrical system". The group will discuss this at a meeting in April, although top exporter Saudi Arabia has said a decision may not be made until another gathering in June.
In the report, OPEC said its oil output fell by 221,000 bpd month-on-month to 30.55 million bpd in February.
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Despite this strong compliance, market indicators followed by OPEC still suggest a glut could appear. That amounts to 105 per cent compliance with pledged cuts, according to a Reuters calculation, up from January's rate. It kept its forecast for growth in global oil demand this year unchanged at 1.24 million bpd.
The US Petroleum Institute said Tuesday that crude oil stocks in the United States unexpectedly fell last week, while gasoline stocks fell and distillate stocks increased.
Brent crude hit a 2019 peak of $68.14 per barrel before falling to $67.93 by 1250 GMT, up $0.38 or 0.56% from Wednesday's close.
International Brent crude oil futures were at $67.37 US a barrel, up 70 cents, or 1.1%, from their last close.
"With OPEC's cuts in full-swing. persistent supply issues and a deteriorating picture on Venezuela, oil is looking well supported", said Jasper Lawler, head of research at futures brokerage London Capital Group.
While it may be just as problematic as the notion of global oversupply that dominated analytical fears until recently, the perception of a tightening market continued to result in gains for crude prices, with USA oil settling a substantial 2.4 percent higher on Wednesday.
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