* Brent up around 20 percent in third quarter
* Turkey calls Kurdistan referendum illegitimate
* Middle East producers worry high price will boost U.S. shale (Updates throughout, changes dateline, previous TOKYO)
AMSTERDAM, Sept 29 (Reuters) - Oil edged higher on Friday as tensions around Iraqi Kurdistan threatened the region's crude supplies, helping Brent prices to their strongest third-quarter performance since 2004.
Global benchmark Brent crude was up 24 cents at $57.65 a barrel at 0911 GMT. The contract had reached its highest in more than two years earlier in the week, resulting in a fifth consecutive weekly gain. This performance is Brent's longest weekly bull run since June 2016.
U.S. crude traded 14 cents higher at $51.70 a barrel, on track for its strongest third quarter in 10 years and its longest streak of weekly gains since January.
Iraq's Kurds endorsed secession by nine to one in a referendum on Monday that has angered Turkey, the central government in Baghdad, and other powers, who fear the vote could lead to renewed conflict in the oil-rich region.
Turkish President Tayyip Erdogan called the vote illegitimate and has threatened to break with past practice and deal only with the Baghdad government over oil exports from Iraq.
"No rapid solution to the crisis can be expected, which should continue to lend support to the oil price," analysts at Commerzbank wrote.
Most oil that flows through a pipeline from Iraq to Turkey comes from Kurdish sources and a cut-off would severely damage the Kurdish Regional Government, which relies on sales of crude for almost all its hard currency revenues.
So far, oil flows through the pipeline have been normal.
Oil price gains have also been supported this month by anticipated renewed demand from U.S. refiners that were resuming operations after shutdowns due to Hurricane Harvey.
However, Middle Eastern oil producers are concerned the recent price rise will incentivise more U.S. shale production and in turn push prices lower again.
(Additional reporting by Aaron Sheldrick in Tokyo; Editing by Dale Hudson)