By Timothy Puko and Georgi Kantchev 

Strong signs for demand helped oil bounce and sent gasoline prices soaring Wednesday.

Demand for crude is increasing at its fastest pace in five years, the International Energy Agency said in its closely watched market report. The report helped calm fears of sluggish demand that had pushed U.S. oil to its lowest settlement in six years on Tuesday.

Gasoline stockpiles in the U.S. fell at a much faster rate than expected last week, the U.S. Energy Information Administration said. BP PLC is also taking down its largest unit at the Whiting, Ind., refinery for about a month, tightening gasoline markets in the Midwest, analysts and a broker say.

Light, sweet crude for September delivery gained 22 cents, or 0.5%, to settle at $43.30 a barrel on the New York Mercantile Exchange. Brent crude, the global benchmark, gained 48 cents, or 1%, to $49.66 a barrel on ICE Futures Europe.

Gasoline futures settled up 6.98 cents, or 4.1%, at $1.7635 a gallon. Prices hit their highest point for August after gains of 8.7% over three sessions. It is among gasoline's sharpest rallies in months.

Gasoline stockpiles fell by 1.3 million barrels in the week ended Aug. 7, EIA said in its weekly report on oil stockpiles. Analysts had expected gasoline supplies to fall by 800,000, and the larger-than-expected draw was the only bullish data in the highly watched gauge of supply and demand.

It showed oil stockpiles shrank by 1.7 million barrels, 19% shy of analysts' expectations for the week ended Aug. 7. Distillates, which include diesel, added 3 million barrels, three times as much as expected. Diesel futures settled up 2.4 cents, or 1.5%, to $1.5869 a gallon.

EIA data also showed imports up 5.2% for the week at 7.6 million barrels a day, despite U.S. production on pace for its highest tally in more than 30 years. That shows a price-cutting war for customers is still alive and well as exporters such as Saudi Arabia are managing to sell crude into the U.S. despite its own high production and a 60% fall in prices since last year, said Kyle Cooper, managing director of research at IAF Advisors, a Houston consulting firm.

"Crude supplies are very, very high," he added, noting that refineries will soon begin maintenance and drain even less from stockpiles. "So those levels are bound to start increasing in the coming weeks."

Despite the short-term setback, the global oversupply of crude may be significantly smaller than some worst-case scenarios suggest, analysts said after reviewing the IEA report. That helped reassure the market after China's plummeting currency had spread fear that global demand won't catch up to rampant supply.

"Oil's plunge below $50 a barrel from triple digits a year ago has seen demand react more swiftly than supply," the IEA said on Wednesday.

The Paris-based agency said global oil demand would grow by 1.6 million barrels a day this year, an upward revision of 200,000 barrels a day from its previous forecast, and would keep rising by 1.4 million barrels a day next year.

The IEA's methodology also suggests the oversupply isn't as bad as some worst-case scenarios suggest, analysts at both Tudor, Pickering, Holt & Co. and Simmons & Co. International said. Some of the stockpiled oil IEA adds to its calculations now is like to shrink over time, analysts at Tudor, Pickering said in their assessment of the report.

"Bottom Line: The market is oversupplied, but closer to" 500,000 barrels a day, not 2.5 million, they added.

EIA just a day ago released updated forecasts showing oversupply at just more than 2 million barrels a day for 2015. The IEA did warn that the oversupply is likely to persist as global production "continues to grow at a breakneck pace."

Oil prices on Wednesday also found support in the weaker dollar. The Wall Street Journal Dollar Index, which tracks the dollar against a basket of other currencies, fell 0.7%. Oil is priced in dollars and it becomes cheaper for holders of other currencies as the dollar falls.

Many people who bet on oil's fall are also likely closing out profitable bets, analysts said. That can bid up prices, a phenomenon called short-covering.

"Not surprised" by the rebound, said Gene McGillian, an analyst at Tradition Energy The "selloff has looked a bit overdone and thinking this is really just light short covering going on."

Many, however, are expecting further selling in the days to come. The IEA said that many in the industry see oil prices staying lower for longer as "muscular pumping" from Saudi Arabia and Iraq, the Organization of the Petroleum Exporting Countries' top producers, is adding to the global glut. The oversupply is likely to is through 2016, longer than many expected, it said.

"It will be difficult for Brent and (U.S.) crude prices to sustain any significant, fundamentally driven rallies for the balance of this year and potentially through" the first half of 2016, Vikas Dwivedi, global energy strategist at Macquarie Group Ltd., said in a note.

Write to Timothy Puko at tim.puko@wsj.com and Georgi Kantchev at georgi.kantchev@wsj.com

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