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UPDATE 2-Oil mixed but set for weekly gain on improving market outlook

* Brent up a fraction, WTI drops

* Analyst says market may "pause for breath" (Adds comment, updates prices)

TOKYO, Sept 29 (Reuters) - Oil prices were mixed on Friday, but both Brent and U.S. crude were set to chalk up another weekly gain as investors bet that efforts to cut a global glut are working and that the demand outlook is improving.

U.S. crude was down 8 cents at $51.48 a barrel at 0641 GMT, after earlier rising slightly. Still, the contract is heading for a fourth consecutively weekly gain and is on track for a 9 percent advance this month.

Brent rose 1 cent to $57.42 a barrel, heading for a fifth weekly climb and a nearly 10 percent gain for September.

The price gains, most of them in the last two-and-a-half weeks, have come as traders anticipated renewed demand from U.S. refiners that were resuming operations after shutdowns due to Hurricane Harvey.

Major world oil producers outside the United States have also indicated they will stick with output cuts to limit supply.

They are getting support from Turkey's threats to cut off a pipeline from the Kurdish region of Iraq after a referendum where Kurds voted overwhelmingly in favor of independence.

"(There is) an increasingly positive view from the supply side, with potential Kurdish production disruption, and a plethora of energy agencies suggesting global demand is increasing," said Jeffrey Halley, senior market analyst at OANDA in Singapore.

"The technical picture still looks positive for both contracts with the consolidation and gentle pull-backs thus far suggesting oil is pausing for breath at these levels," he said.

Turkish President Tayyip Erdogan said this week he could use force to prevent the formation of an independent Kurdish state and might close the oil "tap."

The Kurdish region exports about 500,000 barrels a day through a pipeline that runs through Turkey to the Mediterranean Sea.

Turkey promised on Thursday to deal only with the Iraqi government on crude, the office of Iraqi Prime Minister Haider al-Abadi said. (Reporting by Aaron Sheldrick; Editing by Joseph Radford and Richard Pullin)