UPDATE 3-Oil prices fall 2 percent on signs market still oversupplied

* U.S. crude production rose 1 percent last week - EIA

* U.S. crude inventories fell to lowest since Jan. - EIA

* Russia to continue cooperating to stabilise oil price

* Morgan Stanley sees WTI crude below $50 to mid-2018 (Updates throughout, changes dateline, previous SINGAPORE)

LONDON, July 7 (Reuters) - Oil prices fell more than 2 percent on Friday after data showed U.S. production rose last week just as OPEC exports hit a 2017 high, casting doubt on efforts by producers to curb oversupply.

Global benchmark Brent futures were down $1.07, or 2.2 percent, at $47.04 a barrel at 0929 GMT, after falling to as low as $46.75, its weakest level in more than a week.

U.S. West Texas Intermediate (WTI) crude futures traded at $44.40 a barrel, down $1.12 or 2.5 percent. Their session low of $44.20 was also the lowest in over a week.

"We're seeing some head scratching today. Following a sharp rally, which was mostly driven by short-covering, the failure of Brent to break back above $50 earlier in the week has once again given sellers appetite for sending it lower," said Ole Hansen, head of commodity strategy at Saxo Bank.

Weekly U.S. government data showed on Thursday that U.S. oil production <C-OUT-T-EIA> rose one percent to 9.34 million barrels per day (bpd), correcting a drop in the previous week that was down to one-off maintenance and hurricane shutdowns.

The rise in U.S. output coincides with exports from the Organization of the Petroleum Exporting Countries climbing for a second consecutive month in June to the highest this year.

Russian President Vladimir Putin, whose country is cooperating with OPEC in a deal to stem oil production, said on Friday he wanted to continue cooperating with other countries to reduce price volatility.

The market largely ignored news from the U.S. Energy Information Administration (EIA) that U.S. crude inventories fell by 6.3 million barrels in the week to June 30 to 502.9 million barrels, the lowest since January.

If OPEC was unable to balance the market, change would likely be forced on it by oil prices, said Morgan Stanley.

The U.S. bank said a WTI price of $46 to $50 per barrel would likely prevent U.S. production rising in the mid- to long-term, but "prices will need to be in the low $40s" for U.S. output to fall significantly.

Morgan Stanley said it expected WTI to remain below $50 until mid-2018.

(Additional reporting by Henning Gloystein in Singapore and Aaron Sheldrick in Tokyo; Editing by Edmund Blair)