* Weekly U.S. production rebounds, refining runs down again - EIA
* Gasoline stocks fall by record weekly amount - EIA
* IEA raises forecast for 2017 global oil demand growth (Updates with EIA data, adds quotes, details, changes byline, dateline, previous LONDON)
NEW YORK, Sept 13 (Reuters) - Oil prices rose on Wednesday after the International Energy Agency (IEA) said a global surplus of crude was starting to shrink, even though U.S. data showed another big increase in crude inventories due to the ongoing effects of Hurricane Harvey.
U.S. gasoline and distillate stocks fell sharply as Harvey shut nearly a quarter of the nation's capacity with major Gulf Coast refineries only starting to come back to life in the last few days.
The U.S. Energy Information Administration's weekly data showed a build of 5.9 million barrels of crude, exceeding expectations for a 3.2 million-barrel hike.
Much of that was because of a near 10 million-barrel increase in stocks in the U.S. Gulf region and as crude production rebounded from a brief Harvey interruption.
Oil prices jumped after the report but then pared gains.
U.S. crude futures were up 53 cents, or 1.1 percent, to $48.75 per barrel and Brent crude was up 32 cents to $54.59 a barrel, about where prices were prior to the data.
A sharp rebound in U.S. oil production compared with last week has limited gains in crude prices as concerns grow that oil output is recovering faster than refining capacity coming online," said Abhishek Kumar, senior energy analyst at Interfax Energys Global Gas Analytics in London.
U.S. crude production rebounded to an average of 9.35 million barrels per day from 8.78 million bpd a week earlier, entirely the result of increases in the lower 48 states.
U.S. gasoline stocks slumped 8.4 million barrels, the largest one-week decline since the U.S. Energy Department started recording the data in 1990, while distillate stocks fell 3.2 million barrels.
U.S. gasoline futures dipped after the data, and were down modestly to $1.6546, however, which Andrew Lipow of Lipow Oil Associates in Houston said was a "counterintuitive" reaction.
"The market is reacting in anticipation of refineries restarting at the same time expecting a decline in demand due to the after effects of Hurricanes Harvey and Irma," he said.
The International Energy Agency, in its report, noted that the country's reliance on the Gulf Coast makes it vulnerable to similar events like Harvey, saying "normal operations are too important to fail."
It recommended that the U.S. strengthens its energy security to address events, such as hurricanes, by potentially adding oil products to government-held inventories.
Overall, the IEA said in its monthly report that robust global demand and an output drop from OPEC and other producers should help balance inventories.
The assessment echoed a report by the Organization of the Petroleum Exporting Countries forecasting higher demand for its oil in 2018 and pointing to signs of a tighter global market.
OPEC agreed with non-member nations last year to cut supply by 1.8 million bpd through March 2018, and major nations are seeking to extend that agreement further.
The U.S. EIA on Tuesday revised its 2017 and 2018 U.S. oil output forecasts lower to reflect, in part, the effects of Harvey.
(Additional reporting by Scott DiSavino in New York, Fanny Potkin in London and Aaron Sheldrick in Tokyo; Editing by Marguerita Choy and Louise Heavens)