UPDATE 4-Oil prices fall as OPEC output, U.S. crude stockpiles rise

* OPEC says its oil output up 336,000 bpd at 32.14 mln bpd in May

* U.S. crude stocks rise 2.8 mln barrels to 511.4 mln - API

* Global oil demand growth slows, especially in key market China

* OPEC exports in 2017 vs 2016: http://tmsnrt.rs/2sZPdJT (Adds IEA report details)

LONDON, June 14 (Reuters) - Oil prices fell on Wednesday after industry data showed a build in U.S. crude stocks and OPEC reported a rise in its production despite a pledge to cut output.

Brent crude oil was down 36 cents a barrel at $48.36 by 0941 GMT. U.S. crude was 45 cents lower at $46.01.

Crude prices have fallen more than 10 percent since late May, pulled down by heavy global oversupply that has persisted despite a move led by the Organization of the Petroleum Exporting Countries to curb production.

OPEC and other exporters such as Russia have agreed to keep production almost 1.8 million barrels per day (bpd) below the levels pumped at the end of last year and not to increase output until the end of the first quarter of 2018.

But adherence to the cuts is under scrutiny and the producer group said this week that its output rose by 336,000 bpd in May to 32.14 million bpd.

Oil stocks are near record highs in some parts of the world, and producers that are not part of the OPEC deal are increasing output.

The International Energy Agency on Wednesday said it expected growth in non-OPEC supply to be higher next year than growth in overall global demand.

"For total non-OPEC production, we expect production to grow by 700,000 bpd this year, but our first outlook for 2018 makes sobering reading for those producers looking to restrain supply," the IEA said in its monthly oil market report.

Shale supply has pushed U.S. crude production up by about 10 percent over the last year to 9.3 million bpd - not far below the output of top exporter Saudi Arabia. <C-OUT-T-EIA>

"The outlook for oil hinges on the effectiveness of the OPEC cuts relative to the supply increases from U.S. shale," said William O'Loughlin, analyst at Australia's Rivkin Securities.

Data from the American Petroleum Institute showed on Tuesday that U.S. crude stocks rose by 2.8 million barrels in the week to June 9 to 511.4 million, compared with expectations for a decrease of 2.7 million barrels.

With supplies plentiful, strong demand is needed to support the market, but there are signs of a slowdown.

Global energy demand grew by 1 percent in 2016, a rate similar to the previous two years but well below the 10-year average of 1.8 percent, BP said in its benchmark Statistical Review of World Energy on Tuesday.

Economic expansion in China, a key component of world oil demand growth for many years, is now slowing.

"Chinese demand is slow ... so we have a build-up of crude in Asia where demand seems to have slowed for now," said Oystein Berentsen, managing director of oil trading company Strong Petroleum.

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