UPDATE 9-Oil up for third session on supply problems in Libya, Iraq
* Brent rebounds near 4-month high after sell-off last week
* Unrest, strikes cut Libyan oil exports to two-year low
* API data shows draw in US crude inventories
* Markets watch the Fed for clues on September tapering
By Jeanine Prezioso and Nicolas Medina Mora Perez
NEW YORK, Aug 13 (Reuters) - Oil prices on both sides of the Atlantic rose for a third straight session on Tuesday because of worries over supplies from OPEC nations Libya and Iraq.
Brent crude moved back toward a four-month high near $110 a barrel following last week's sell-off, while U.S. crude hit the highest level in six sessions, rising above $107.
Labor unrest in Libya has forced oil output to its lowest since the 2011 civil war, with the country's total oil production well below 500,000 barrels per day (bpd) from 1.3 million bpd in June.
This sparked fear of a possible supply shortfall in the northern hemisphere and boosted prices, analysts said.
Libya's state National Oil Corp. said in a statement to shippers that it could not provide September loading schedules, normally due by now, as on-again, off-again strikes paralyse its ports.
The disruptions can be "manageable" if Saudi Arabia maintains high production, said Sarah Emerson, managing director of Energy Security Analysis Inc in Wakefield, Massachusetts.
"The question is how long does it last. Today it's manageable."
Richard Mallinson, chief policy analyst at London-based consultancy Energy Aspects, told Reuters Global Oil Forum, that output was around 400,000 bpd and exports at around 300,000 bpd. Libya has the capacity to produce about 1.6 million bpd.
Maintenance work at Iraq's key southern oil export hub is also expected to cut supplies by 500,000 bpd in September, lending further support to prices in the medium term.
Front-month Brent crude oil futures for September delivery rose 85 cents to settle at $109.82 a barrel after touching an intraday high of $110.06, its highest since it hit a four-month high of $110.09 on Aug. 2.
Brent rose back above its 200-day moving average on Monday at $108.17, a technical marker watched by traders. The contract also fully breached the short-term 10-and-15 day moving averages on Tuesday.
Trading in CME Group Inc's New York Mercantile Exchange Brent crude oil contract set a record on Tuesday, the exchange said, at 104,839 contracts, eclipsing the previous high of 90,390 reached late last week.
Higher oil prices are already taking a toll on oil refiners in Europe that are expected to cut processing rates by about 500,000 bpd this week due to poor profit margins.
In the United States, front month crude oil futures rose 72 cents to settle at $106.83 a barrel after trading as low as $105.56 during the session. U.S. crude's discount to Brent settled at $2.99 a barrel.
Traders said prices were supported after the U.S. National Hurricane Center said a tropical wave in the Caribbean might become a cyclone in the oil-producing Gulf of Mexico in the coming days.
The American Petroleum Institute's weekly report showed on Tuesday that U.S. crude oil stockpiles fell last week, although the decrease in inventories was smaller than expected.
The industry group said that U.S. crude oil stocks fell by 900,000 barrels last week, compared to the 1.5 million barrel draw forecast by a Reuters poll.
Stocks of crude at the Cushing, Oklahoma, delivery point of the U.S. oil future fell by 1.4 million barrels, marking the sixth straight week of draws.
The market's immediate reaction to the data was muted, with prices remaining close to settlement levels in after-hours trading.
Traders were also looking for hints on the timeline of the Federal Reserve's plans to cut its stimulus spending program.
Echoing earlier statements by other officials, Atlanta Fed President Dennis Lockhart said on Tuesday that the central bank could begin tapering its bond-buying policies as early as September, despite lower-than-expected inflation levels, but it would only be a "cautious first step" while economic data remains mixed.