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UPDATE 6-Oil rises after signs of U.S. demand, but supply threat remains

* 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 prices)

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 slide, although the prospect of oversupply in 2018 prompted yet more analysts to cut their price forecasts.

Brent crude futures were up 76 cents on the day at $48.55 a barrel by 1307 GMT. The price fell as much as 4.6 percent on Wednesday, before closing down 3.7 percent, its biggest one-day drop in a month.

U.S. West Texas Intermediate crude futures were up 79 cents at $45.92 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 forecasts 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 output.

Weekly inventory figures from the U.S. Energy Information Administration (EIA) could confirm the hefty drop in crude stocks, thereby giving the oil price scope to rally further.

"If the EIA confirms the API figures, or better still comes in even stronger, then there is a potential for oil prices to completely reverse yesterday's drop," said Fawad Razaqzada, an analyst at Forex.com.

"However, the bar is raised now and the scope for disappointment is high. Thus, if the EIA data contradicts the API estimates, then expect the opposite reaction in oil prices."

Bank of America Merrill Lynch this week joined a chorus of analysts that have cut their outlook for crude prices.

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.

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.

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