* Iraqi Kurdistan oil flows to Turkey rise - source
* U.S. crude inventories expected to fall for 5th week
* API report on U.S. inventories due at 2030 GMT (Changes dateline from TOKYO, updates prices, adds quote)
LONDON, Oct 24 (Reuters) - Oil fell towards $57 a barrel on Tuesday as crude flows through Iraq's northern pipeline to Ceyhan in Turkey rose further, offsetting an expected fall in U.S. crude inventories.
Pumping along the pipeline rose to 300,000 barrels per day on Tuesday, a shipping source said, adding to a gain on Monday. Output fell from 600,000 bpd last week when Iraqi forces retook control of oilfields from Kurdish fighters.
"The increase is minimal and is way below the normal 600,000 bpd, nevertheless the market took it as a positive development as far as oil supply is concerned," said Tamas Varga of oil broker PVM, referring to the gain in flows on Monday.
Brent crude, the global benchmark, was down 16 cents at $57.21 by 0853 GMT. It reached $59.49 on Sept. 26, its highest since July 2015. U.S. crude fell 12 cents to$51.78.
The disruption to exports from Iraq, the second-largest producer in OPEC, has helped support the market, adding to the supply cut being carried out by OPEC and allied producers since January to get rid of excess supply.
Shipments from the north and south of Iraq in October have fallen more than 200,000 bpd, according to export data and an industry source, although Iraq is hoping to boost southern exports to compensate for the northern drop.
That should give OPEC's already high compliance with the cutback agreement a boost. In September, the OPEC and non-OPEC countries participating in the supply cut met 120 percent of their commitments, OPEC said.
OPEC and its allies are hoping to drain excess supply that is keeping prices at half their level of mid-2014. In a further sign that the glut is easing, analysts expect U.S. crude inventories to decline by 2.5 million barrels in the latest weekly supply reports.
Industry group American Petroleum Institute (API) is scheduled to release its data at 2030 GMT on Tuesday and the government's Energy Information Administration reports on Wednesday.
(Addiitonal reporting by Osamu Tsukimori; Editing by Susan Fenton)