* Turkey says will deal only with Iraq on crude exports
* No interruption yet to oil flows from Iraqi Kurdistan
* Investors trim crude holdings after sharp gains (Updates throughout, changes dateline, previous TOKYO)
LONDON, Sept 28 (Reuters) - Oil prices steadied on Thursday, taking a breather after gains spurred by rising tension in northern Iraq following the semi-autonomous Kurdistan region's vote for independence in a referendum.
Brent crude oil was unchanged at $57.90 a barrel by 0850 GMT. It hit a more than two-year high of $59.49 on Tuesday after Monday's referendum vote prompted Turkey to threaten to close the region's oil pipeline, before pulling back.
U.S. light crude was 5 cents higher at $52.19 after rising 26 cents on Wednesday to just below a five-month high.
"Profit taking and the fact that Kurdish oil exports seem unaffected by the referendum pushed crude lower," said Tamas Varga, analyst at London brokerage PVM Oil Associates.
"But I think the market will strengthen again. Kurdistan and Northern Iraq now export 500,000-550,000 barrels per day (bpd). That would be a big loss to the market," Varga added.
Iraqi Kurdistan voted overwhelmingly on Monday in favor of independence, prompting Turkish President Tayyip Erdogan to say he could use military force to prevent the formation of an independent Kurdish state and might close the oil "tap."
Turkey said on Thursday it would deal only with the Iraqi government on crude oil exports, "restricting oil export" operations to Baghdad.
U.S. crude prices found some strength from a surprise fall in U.S. stocks.
U.S. crude inventories fell 1.8 million barrels last week, the U.S. Energy Department said, versus forecasts for a 3.4 million-barrel build.
U.S. refiners are still returning to full operations after Hurricane Harvey last month, but gasoline stocks surprisingly rose and stocks of distillates fell less than anticipated.
While this week's U.S. data gave a mixed picture, the outlook for global oil demand has strengthened, analysts say.
The International Energy Agency earlier this month raised its 2017 global oil demand growth estimate to 1.6 million barrels per day (bpd) from 1.5 million bpd, citing stronger-than-expected demand growth in the United States and Europe.
Still, U.S. crude production rose to 9.55 million bpd last week, higher than before Harvey hit the Gulf Coast.
With Brent futures commanding their highest premium over U.S. crude <WTCLc1-LCOc1> in more than two years, U.S. crude has become increasingly competitive in foreign markets and exports hit a record 1.5 million bpd last week.
That complicates efforts by the Organization of the Petroleum Exporting Countries and other major producers to push oil higher through output curbs, as every hike in price encourages more U.S. production. (Additional reporting by Aaron Sheldrick in Tokyo; Editing by Susan Fenton)