Another influence for traders was USA sanctions against oil exports from Iran and Venezuela said to be contributing to the tightening: Barclays noted that "Failures in [Venezuela's] electrical system". This was led by a drop in supply from Venezuela - exempt from the Opec cut but under USA sanctions - and a further voluntary reduction by Saudi Arabia.
West Texas Intermediate Crude oil futures for April ended up $1.39, or 2.4%, at $58.26 a barrel, the highest settlement in four months.
Brent and West Texas Intermediate crude oil futures reached four-months highs on Thursday, as a production curb agreement by OPEC and its partners along with US sanctions on Iran and Venezuela tightened global supplies.
OPEC sources have said an extension of the supply-cutting pact is the likely scenario.
EIA expects these trends to continue over the next several years.
Two sources told Reuters that the USA also aims to curb Iran's crude exports by about 20% to below 1 million barrels per day (bpd) from May, likely reining in waivers for Tehran's remaining customers.
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Global benchmark Brent crude was trading at $66.94 per barrel at 0708 GMT with a 0.2 percent gain, after it closed Tuesday at $66.81 a barrel.
Crude inventories dropped by 3.9 million barrels in the last week, to 449.07 million barrels, compared with analyst expectations for an increase of 2.7 million barrels.
Forecasts slowed USA production to a record of 13 million barrels per day (bps) until the third quarter of 2020, instead of the second quarter of previous forecasts.
Oil exports at 3.5m b/d, production 4.5m b/d.
"While oil demand is expected to grow at a moderate pace in 2019, it is still well below the strong growth expected in the non-OPEC supply forecast for this year", OPEC said in the report. 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. Crude oil imports to the United States fell last week by 523,000 bpd to 6.4 million bpd.