* U.S. crude stocks down by 5.8 mln barrels to 503.7 million - API
* But global markets remain well supplied as OPEC exports rise
* Analysts reduce Brent crude oil price forecasts
By Henning Gloystein
SINGAPORE, July 6 (Reuters) - Oil prices nudged higher early on Thursday, supported by strong demand in the United States, but analysts cautioned that the outlook was for lower prices due to oversupply.
Brent crude futures, the international benchmark for oil prices, rose 28 cents, or 0.6 percent, to $48.07 per barrel by 0132 GMT.
U.S. West Texas Intermediate (WTI) crude futures were at $45.39 per barrel, up 26 cents, or 0.6 percent.
Traders said the gains reflected firm fuel demand in the United States, where data from the American Petroleum Institute (API) late on Wednesday showed that U.S. crude inventories fell by 5.8 million barrels in the week to June 30 to 503.7 million.
However, overall market conditions remain weak.
Crude prices tumbled about 4 percent on Wednesday on rising exports by the Organization of the Petroleum Exporting Countries (OPEC), despite its pledge to hold back production between January this year and March 2018 to prop up prices.
OPEC's oil exports rose for the second month in a row in June, according to Thomson Reuters Oil Research.
OPEC exported 25.92 million barrels per day (bpd) in June, 450,000 bpd above May and 1.9 million bpd more than a year earlier.
Energy research house and brokerage firm Sanford C. Bernstein said it was reducing its average Brent crude oil price forecasts for 2017 and 2018 to $50 per barrel each, down from $60 and $70 previously.
Bernstein said that the reduction was a result of an expected increase in U.S. shale oil output, especially from the Permian field.
"Permian supply pummels our near term estimates," Bernstein said, adding that conventional supply additions would likely exceed or match production declines of mature fields.
Denmark's Saxo Bank said that oil prices could rise towards $55 per barrel in the coming months, but said it expected lower prices towards the end of the year and into 2018.
"The price of Brent crude oil is likely to rally back towards $55 per barrel during the coming months before renewed weakness sets in as the focus turns to 2018 and the potential risk of additional barrels hitting the market if OPEC and Russia fail to extend the production cut deal beyond Q1 2018," Ole Hansen, Head of Commodity Strategy at Saxo Bank, said in a quarterly market outlook.
Reporting by Henning Gloystein; Editing by Joseph Radford and Richard Pullin