* Easing fear of imminent U.S. attack on Syria soothes nerves
* Oil set for biggest weekly gain since July
* OPEC sees oil markets tightening even as U.S. produces more
* China March crude oil imports 2nd highest on record (Updates prices, adds details)
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 eight months.
NYMEX crude for May delivery was down 16 cents, or 0.2 percent, at $66.91 a barrel at 0632 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 18 cents, or 0.2 percent, at $71.84, and is up about 7 percent for the week.
Both benchmarks, which have risen about $5 this week, are set for their biggest weekly gains since last July. They surged to their highest 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.
Trump tweeted on Thursday 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.
"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. That's not to say that we can't go up just based on fundamentals because the market supply-demand is tight."
OPEC said on Thursday a global oil stocks surplus is close to evaporating, and that its collective output fell 201,000 barrels per day to 31.96 million bpd in March from February.
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.
The potential reintroduction of sanctions on Iran was unlikely to have an immediate impact on the oil market, Goldman Sachs said on Thursday.
President Trump has given European signatories a May 12 deadline to "fix the terrible flaws" of a 2015 nuclear deal or he will refuse to extend U.S. sanctions relief on Iran.
Meanwhile China's March crude oil imports climbed from a month earlier to the second highest on record, calculated on a daily basis, as refiners replenished stocks on generous government quotas and ahead of peak maintenance season.
(Reporting by Osamu Tsukimori Editing by Richard Pullin and Kenneth Maxwell)