* U.S. crude inventories show surprise build - EIA
* U.S. gasoline, distillate stocks fall by more than 5 mln bbls
* Southeast Asia crude imports to more than double by 2040 - IEA (Updates detail, prices; paragraphs 1-3)
LONDON, Oct 26 (Reuters) - Oil slipped on Thursday, pressured by an unexpected increase in U.S. crude inventories, high U.S. production and exports, but stayed near multi-month highs on support from tighter crude markets.
Brent crude was down 35 cents at $58.09 a barrel by 1335 GMT. The global benchmark is not far below its 26-month high of $59.49 hit in late September.
U.S. light crude was 10 cents lower at $52.08.
Markets have been supported by comments from Saudi Arabia's energy minister earlier this week reiterating the kingdom's determination to end a global supply glut that has weighed on prices for more than three years.
Crude oil for immediate lifting has moved to a premium over later futures prices, indicating that demand for oil is strong in many of the biggest consuming regions, including Europe.
Oil prices have been rising for weeks and some investors have begun to take profits, brokers say.
"The trend is up, but getting tired," said Robin Bieber, technical chart analyst and a director of London brokerage PVM Oil Associates.
U.S. crude inventories rose by 856,000 barrels last week, U.S. Energy Information Administration (EIA) data showed. Analysts had expected a fall of 2.6 million barrels.
U.S. gasoline and heating oil futures contracts rallied after the EIA data showed inventories of gasoline and distillate fuel, which includes heating oil and diesel, both fell by more than 5 million barrels. The fuel inventories dropped despite a rise in refining output.
U.S. crude production rose 1.1 million barrels per day (bpd) last week to 9.5 million bpd after a decline due to Hurricane Nate, while U.S. crude oil exports hit a new record four-week average of 1.7 million bpd.
But higher U.S. supply has been balanced by worries over crude exports from the Middle East.
Crude shipments to Turkey from northern Iraq, the second-largest producer in the Organization of the Petroleum Exporting Countries, have declined after Iraqi government forces took back the city of Kirkuk last week after a Kurdish referendum on independence.
Some of the concern around oil exports from the northern part of Iraq eased after Kurdish authorities offered to suspend their independence referendum and proposed ceasefire.
Meanwhile, global oil demand keeps rising.
Southeast Asia's net crude oil imports will more than double to 5.5 million bpd by 2040 as the region adds new refining capacity to meet rising demand while regional oil output falls, according to the International Energy Agency (IEA).
(Additional reporting by Osamu Tsukimori in Tokyo; Editing by Jon Boyle and Adrian Croft)