Oil futures were under pressure Wednesday, with signs of weakening global demand and nervousness over U.S. supply data overshadowing price-supportive tensions between the U.S. and Iran.

West Texas Intermediate crude for June delivery CLM9, -0.66%  fell 61 cents, or 1%, to $61.79 a barrel, while the global benchmark, July Brent LCON9, -0.17% was off 52 cents, or 0.7%, to $70.72 a barrel.

The American Petroleum Institute, an industry group, late Tuesday said U.S. crude supplies rose 8.6 million barrels in the week ended May 10, according to sources. The API was also showed gasoline inventories rose 567,000 barrels, while distillates increased by 2.2 million barrels, sources said.

The Energy Information Administration’s more closely followed data will be released Wednesday morning. Analysts surveyed by The Wall Street Journal expect crude supplies to have fallen 1.4 million barrels last week.

Meanwhile, the International Energy Agency trimmed its forecast for oil-demand growth for 2019 by 90,000 barrels a day to 1.3 million barrels, but said it expected the slower growth to be short-lived.

“The API report was very bearish, with storage builds across the board. Crude Oil storage was up a whopping 8.63 million versus my above average forecast of a build of 2.5 million, and storage at the NYMEX delivery site at Cushing was up 2.06 million. The IEA monthly report was also bearish, with demand projections taking a hit,” said Robert Yawger, director of energy trading at Mizuho Securities U.S.A.

Analysts said downside could remain limited amid worries over the Middle East. The U.S. on Wednesday ordered all nonemergency staff to leave Iraq immediately amid heightened tensions with Iran over recent attacks against oil tankers and facilities in the Persian Gulf region.

See: U.S. claims of growing Iranian threat met with global skepticism

While the aggressive stance toward Iran “has clearly added an element of strong geopolitical unease to the world’s major oil exporting region, and if it weren’t for strong U.S. supply growth and a sluggish economic/demand performance, even the tentatively price-cautious JBC Energy Research Center would have expected prices to rally much more and set new year-to-date highs,” wrote analysts at JBC Energy, a Vienna-based consulting firm, in a note.

“But let’s not forget, on the thus-far-still-minor-chance of a full escalation in the Middle East, there is not much that would stop prices from reaching the highs of last year and maybe even spike beyond,” they said.

In energy products trade, June gasoline RBM9, +0.15%  fell 0.54 cent, or 0.3%, to $1.9713 a gallon, while June heating oil HOM9, +0.46%  was off 0.31 cent, or 0.2%, to $2.0558 a gallon.

June natural-gas futures NGM19, -1.43%  were up 0.1 cent, or less than 0.1%, at $2.66 per million British thermal units.

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