* Brent hits highest since July 2015
* Turkey threatens to cut supply from Iraq's Kurdish region
* Oil market rebalancing continues, inventories falling (Recasts, updates prices, adds comment)
LONDON, Sept 26 (Reuters) - Brent oil prices fell on Tuesday after investors took profit following a rally to 26-month highs spurred largely by threats from Turkey to cut crude exports from Iraq's Kurdistan region.
Brent crude futures fell 85 cents to $58.17 a barrel by 1405 GMT, having hit $59.49, the highest since July 2015 and more than 34 percent above their 2017 low.
U.S. crude futures slid 54 cents to $51.68 a barrel, after hitting a five-month high of $52.43.
Turkish President Tayyip Erdogan repeated a threat to cut off the pipeline that carries 500,000-600,000 barrels per day (bpd) of crude from northern Iraq to the Turkish port of Ceyhan, intensifying pressure on the Kurdish autonomous region over its independence referendum.
This potential loss, combined with 1.8 million bpd of output reductions by the Organization of the Petroleum Exporting Countries and non-OPEC producers, raised concerns of tighter supply.
The Iraqi government said it will not hold talks with the Kurdistan Regional Government about the results of the referendum, which is expected to show a comfortable majority in favour of independence after the results are announced later this week.
"Although there was plenty of price-bullish news making headlines yesterday, undoubtedly the biggest factor was the referendum in the Kurdistan region of Iraq," analysts at Vienna-based JBC Energy said in a note.
But the rally over the past two days also led to profit-taking.
"There's some nervousness at that flat price level given the level of speculative length in the market," Petromatrix strategist Olivier Jakob said.
"We prefer to take a pause at $60.00 a barrel (for) Brent," he wrote in a note.
Top oil executives gathered at the S&P Global Platts APPEC conference in Singapore said strong oil demand this year was accelerating market rebalancing and helping inventory drawdowns.
"Global demand growth is way higher than what we have observed in the last couple of years, coming somewhere close to 1.6 to 1.7 million barrels per day and is driven by distillates," said Janet Kong, BP's chief executive officer, supply and trading, Eastern Hemisphere.
However, other analysts were sceptical about further price gains due to higher oil output from the United States.
The U.S. Energy Information Administration said production from wells in shale formations would rise for a 10th month in a row in October.
U.S. shale producers' ability to ramp up output as later-dated crude prices strengthen will keep price volatility low, said Jeffrey Currie, Goldman Sachs' head of global commodities research. (Additional reporting by Osamu Tsukimori in Tokyo; Editing by Dale Hudson and Louise Heavens)