* U.S., Iranian presidents speak by phone
* Obama says "unique opportunity" to make progress with Iran
* US, Russia agree on Syria resolution; U.N. to vote Friday (Releads with Obama, Rouhani phone call; updates prices to settlement)
By Anna Louie Sussman and David Sheppard
NEW YORK, Sept 27 (Reuters) - Oil fell on Friday as tensions eased between the United States and Iran, culminating in the first phone call between the two countries' presidents since 1979 and a pledge to work swiftly toward an agreement on Iran's nuclear program.
U.S. President Barack Obama said there was a "unique opportunity" to make progress on longstanding tension around Iran's nuclear program, which has led to western sanctions against the country that have curtailed its oil exports.
"It is setting up to be a very bearish event for the market," said John Kilduff, partner at hedge fund Again Capital LLC in New York, adding that Iran appeared ready to "cut a deal".
Brent crude oil for November slipped 58 cents to settle at $108.63, and extended losses to almost $1 a barrel in post-settlement trading following Obama's comments on Iran.
Brent's fall capped the third straight week of losses for international benchmark, with prices dropping by about 7 percent since hitting a six-month high above $117 in early September.
U.S. crude for delivery in November also fell in choppy trading, finishing the session down 16 cents to reach $102.87. The U.S. benchmark hit a session low of $102.36, near its 100-day moving average of $101.99.
Obama's comments followed optimistic remarks earlier Friday from Iranian President Hassan Rouhani, who said he wanted talks with major powers on Iran's nuclear program to yield "tangible results" in a short period of time, revived the prospect of an eventual flow of Iranian crude to the market.
The West's standoff with Iran over the OPEC nation's nuclear program has buoyed oil prices for nearly a decade. Years of sanctions have cut Iranian oil exports by more than 1 million barrels per day (bpd).
Additional diplomatic strides cut further into the geopolitical risk premium in oil markets on Friday, including "constructive" talks in Vienna on Iran's nuclear program and a U.N. agreement on Syria's chemical weapons.
Brent rose briefly around 10:15 a.m. EDT (1415 GMT) following a report that workers at the 210,000-barrel-per-day refinery in Grangemouth, Scotland voted in favor of strike action, raising fears of disruption to North Sea oil supplies.
The Grangemouth refinery is essential to the operation of a major pipeline carrying Forties crude from the North Sea, one of the four crudes that underpins the Brent benchmark.
A strike at the refinery in 2008 led to the temporary shutdown of up to 70 North Sea platforms and the loss of around 700,000 bpd in oil production.
Gains were short-lived, however, as traders focused on improved supplies from the Middle East.
Libya's crude oil output has stabilized at around 650,000 bpd after its western fields resumed production this month but the main eastern oil facilities remain closed, a senior National Oil Corp (NOC) official said.
A Reuters poll of 32 analysts showed Brent crude is expected to average $107.70 a barrel this year.
The North Sea benchmark, which peaked above $117 a barrel in August on concerns the war in Syria would spiral out of control and hit Middle East oil output, has traded at an average of $108.49 per barrel so far this year.
Although Syria is not a major oil producer, any escalation of tension in the Middle East could disrupt flows from a region that supplies nearly a third of the world's oil.
"There's no worry about supply in Brent, there's no major worry about U.S. crude either, so the biggest problem we're looking at is the geopolitical front," said Dan Flynn, a trader and analyst at the Price Futures Group in Chicago, Illinois. (Additional reporting by Robert Gibbons in New York, Christopher Johnson in London, Jacob Gronholt-Pedersen in Singapore; Editing by James Jukwey, Keiron Henderson, David Gregorio and Marguerita Choy)