* Easing fear of imminent U.S. attack on Syria soothes nerve
* Oil set for biggest weekly gain since July
* OPEC sees oil markets tightening even as U.S. produces more (Updates prices, adds details, links)
TOKYO, April 13 (Reuters) - Oil prices edged lower on Friday after U.S. President Donald Trump tempered remarks warning of an imminent missile attack on Syria, but were still set for their biggest weekly gains in more than 8 months.
NYMEX crude for May delivery was down 21 cents, or 0.3 percent, at $66.86 a barrel at 0329 GMT. For the week, the contract is set to post a gain of nearly 8 percent, following two weeks of declines.
London Brent crude was down 24 cents, or 0.3 percent, at $71.78, and is up about 7 percent for the week.
Both benchmarks are set for their biggest weekly gains since last July after surging to a more than three-year high earlier in the week on tensions over Syria and shrinking global oil inventories.
"This last jump of $5 or so is because of the geopolitical situation caused by the situation in Syria," said Tony Nunan, senior oil risk manager at Mitsubishi Corp in Tokyo.
"It looks like Trump backed off a little bit and wants to build a coalition, sending a signal to the broader market that he is going to be much more careful than people thought."
Oil prices hit their highest level since late 2014 on Wednesday after Trump warned that missiles "will be coming" in response to the attack in Syria and Saudi Arabia said it intercepted missiles over Riyadh, both of which raised concerns about possible supply disruptions.
Trump tempered his comments on Thursday and even as he consulted allies such as Britain and France, who could join in any U.S.-led strikes on Syria, there were signs of efforts to prevent the crisis from spiralling out of control.
Trump tweeted an attack on Syria "could be very soon or not so soon at all," raising the prospect that an attack might not be as imminent as he seemed to suggest the day before.
On fundamentals, OPEC said on Thursday a global oil stocks surplus is close to evaporating, citing healthy energy demand and its own supply cuts, while revising up its forecast for production from rivals who have benefited from higher oil prices.
OPEC and its oil producer allies are poised to extend their supply-cutting pact into 2019 even as a global glut of crude is set to evaporate by September, OPEC Secretary-General Mohammad Barkindo told Reuters.
China's crude oil imports rose to 9.2 million barrels per day in March, the second highest on record, according to Reuters calculations based on official customs data.
(Reporting by Osamu Tsukimori; editing by Richard Pullin)