* Surprise U.S. oil output fall supports crude markets
* U.S. crude stocks drop below five-year average
* U.S. fuel inventories register bigger than expected gains
* Asian refinery margins weaken
* Iraq and Iran cut physical crude prices to stay competitive (Updates prices)
LONDON, Jan 11 (Reuters) - Oil prices pulled back from multi-year highs reached earlier in the day on Thursday as warnings grew that a 13 percent rally since early December was close to running its course.
Brent crude futures were flat from the previous day at $69.20 a barrel at 1407 GMT. In earlier trading, it hit $69.62, its highest since an intra-day spike in May 2015 and just two cents away from the highest since 2014.
U.S. West Texas Intermediate (WTI) crude futures were at $63.84, up 27 cents. The contract reached a high of $64.08 per barrel earlier in the day, its highest since December 2014.
Sentiment was boosted by a surprise drop in U.S. production and lower U.S. crude inventories in official data on Wednesday.
"The undeniable fact is that (U.S.) crude oil inventories are at their lowest level since August 2015," said PVM Oil Associates analyst Tamas Varga. "OPEC is edging ever closer to its desired target of reducing OECD industrial stocks to the five-year average."
Data from the U.S. Energy Information Administration on Wednesday showed that crude inventories <C-STK-T-EIA> fell by almost 5 million barrels to 419.5 million barrels in the week to Jan. 5.
U.S. production also fell by 290,000 barrels per day (bpd) to 9.5 million bpd, the EIA said, despite expectations of output breaking through 10 million bpd.
The drop, likely to be because of extreme cold weather that halted some onshore output in North America, was expected to be shortlived.
But on Thursday UAE oil minister and current OPEC President Suhail al-Mazrouei said he expects the market to balance in 2018 and that the producer group is committed to its supply reduction pact until the end of this year.
Production cuts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia, which started in January last year and are set to continue throughout 2018, have underpinned prices.
Still, downward pressure emerged in the physical market, where OPEC's second and third-largest producers, Iran and Iraq, this week cut their prices to remain competitive.
Fuel inventories in Asia and the United States remain ample and in some cases are rising.
U.S. gasoline stocks climbed by a bigger than expected 4.1 million barrels, EIA data showed.
In Asia's Singapore oil trading hub, average refinery profit margins <DUB-SIN-REF> have fallen below $6 a barrel, their lowest seasonal level in five years.
"Markets are getting a bit fatigued and a healthy correction could be on the cards," said Stephen Innes, head of trading for Asia/Pacific at futures brokerage Oanda in Singapore.
(Additional reporting by Henning Gloystein in Singapore; Editing by David Goodman and Mark Potter)