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UPDATE 4-Oil rises after U.S. inventory drop but outlook remains gloomy

* U.S. crude stocks fall 5.8 mln barrels to 503.7 mln-API

Global markets well supplied as OPEC exports rise

* BAML, Bernstein, Saxo Bank cut oil price forecasts (Updates throughout with comment, refreshes prices; changes dateline from SINGAPORE)

By Amanda Cooper

LONDON, July 6 (Reuters) - Oil rose on Thursday, recovering some ground after a surprisingly upbeat picture of U.S. demand halted the previous day's steep slide, although the prospect of oversupply in 2018 has prompted yet more analysts to cut their price forecasts.

Brent crude futures were up 71 cents on the day at $48.50 a barrel. The price fell as much as 4.6 percent at one point on Wednesday, before closing down 3.7 percent, its biggest one-day drop in a month.

U.S. West Texas Intermediate crude futures were also up 71 cents, at $45.84 a barrel.

Data from the American Petroleum Institute (API) on Wednesday showed U.S. crude inventories fell more sharply than expected, down 5.8 million barrels in the week to June 30, against expectations for a draw of 2.3 million barrels.

This comes on the heels of last week's set of data releases that painted a less worrying picture of supply in the United States, where crude output has moderated.

"A change in fortunes is afoot this morning as the energy complex recoups some losses after an upbeat report from the API on U.S. petroleum stocks," PVM Oil Associates analyst Stephen Brennock said in a note.

The oil price is heading for a 1.3 percent rise this week, but has tumbled from one-month highs just below $50 following evidence of rising exports and increased production from the Organization of the Petroleum Exporting Countries, despite the group's commitment to bolster the market by cutting production.

"Against expectations, OECD total oil inventories are still above 3 billion barrels and the recovery in Libyan and Nigerian supplies, coupled with a fast return of U.S. shale, should prevent steep stock draws ahead," Bank of America Merrill Lynch said, adding that output was set to rise further.

The bank cut its average Brent forecasts to $50 this year and $52 per barrel in 2018, from $54 and $56 before.

Bernstein Research reduced its average Brent forecasts for 2017 and 2018 to $50 per barrel each, from $60 and $70 previously.

Bernstein said the reduction resulted from an expected increase in U.S. shale oil output.

Denmark's Saxo Bank said oil prices could rise towards $55 in coming months, but it expected lower prices towards the end of the year and into 2018, especially if OPEC and Russia fail to extend their production cut beyond the first quarter of 2018.

(Additional reporting by Henning Gloystein in SINGAPORE; Editing by Dale Hudson)