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UPDATE 6-Oil prices fall more than 3 pct on signs market still oversupplied

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

Russia says ready to consider revising output deal parameters

* Baker Hughes rig count expected 1 p.m. EDT

* Morgan Stanley sees WTI crude below $50 to mid-2018 (Adds context and quotes, updates byline and prices, changes dateline from LONDON)

By Julia Simon

NEW YORK, July 7 (Reuters) - Oil prices fell more than 3 percent on Friday after data showed U.S. production rose last week just as OPEC exports hit a 2017 high, casting doubt over efforts by producers to curb global oversupply.

Benchmark Brent futures were down $1.55, or 3.2 percent, at $46.56 a barrel at 11:50 a.m. EDT (1550 GMT), after falling to $46.28, the cheapest in more than a week.

U.S. West Texas Intermediate (WTI) crude futures traded at $44.05 a barrel, down $1.47 or 3.2 percent, also the lowest in over a week.

Both benchmarks were set for weekly drops of more than 2 percent.

"The stream of relentless supply continues," said Matt Smith, director of commodity research at Clipperdata.

He noted OPEC exports were 2 million barrels a day higher in June than in 2016, despite a May extension of a 1.8 million barrel production cut led by the Organization of the Petroleum Exporting Countries.

"Weve seen exports last month from OPEC much stronger than they were in April and May, seemingly indifferent to the OPEC production cut deal," Smith said.

Reuters oil data showed OPEC production is now at the highest level this year.

Russia, which is cooperating with OPEC in a deal to stem production, said on Friday it was ready to consider revising the parameters of the deal if need be.

A group of oil producing countries monitoring the output deal will meet on July 24 in Russia, when they could recommend adjusting the pact.

OPEC sources welcomed Russia's comments on Friday, saying they provided a good basis for discussions on deepening production cuts.

Weekly U.S. government data showed on Thursday that U.S. oil production <C-OUT-T-EIA> rose 1 percent to 9.34 million barrels per day (bpd), correcting a drop in the previous week that was due to one-off maintenance work and hurricane shutdowns.

"U.S. producers continue to find economic and cost-efficient ways to put oil on the market," said Rob Haworth, senior investment strategist at U.S. Bank Wealth Management.

At 1 p.m. EDT energy services company Baker Hughes will release rig count data from U.S. drillers.

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.

Morgan Stanley said WTI prices need to be "in the low $40s" for U.S. output to fall significantly.

The U.S. bank said it expected WTI to remain below $50 until mid-2018. (Additional reporting by Karolin Schaps in London, Henning Gloystein in Singapore and Aaron Sheldrick in Tokyo; Editing by Greg Mahlich and Chris Reese)