* OPEC and IEA see oil markets tightening
* China March crude oil imports second-highest on record
* U.S. drillers add oil rigs for second week -Baker Hughes (Updates prices, adds data from Baker Hughes)
NEW YORK, April 13 (Reuters) - Oil prices rose on Friday and were headed for their largest weekly gain since July, amid support from concerns over the prospect of Western military action in Syria and reports of dwindling global oil stocks.
The prospect of military action in Syria that could lead to confrontation with Russia hung over the Middle East but there was no sign a U.S.-led attack was imminent.
Traders sought to lock in long crude positions ahead of the weekend, said John Kilduff, Partner at hedge fund Again Capital Management.
"The geopolitical jitters just keep getting priced in here more and more, as we get closer to the moment of the strikes, if there are any," Kilduff said, noting Syria posed a risk to global stability because of its relationship with other powerful oil producers.
"Syria is a client state of both Russia and Iran and the risk for escalation is quite high and I think that is what the market is worried about."
Brent crude recovered from losses early in the session and was up 67 cents to $72.69 a barrel, and set for about a $5 weekly gain, or 8 percent.
U.S. West Texas Intermediate (WTI) crude futures rose 36 cents to $67.43 a barrel, up 8 percent for the week.
On Wednesday, both oil benchmarks hit their highest since late 2014 after U.S. President Donald Trump warned missiles "will be coming" in response to a suspected gas attack in Syria and after Saudi Arabia said it intercepted missiles over Riyadh.
On Thursday, Trump tweeted that an attack on Syria "could be very soon or not so soon at all."
"The Syrian escalation risk cannot be fully written off, but we view that it deserves less of a premium than three days ago," Petromatrix said in a note.
A global oil stocks surplus is close to evaporating, OPEC said on Thursday, adding its collective output fell to 31.96 million barrels per day (bpd) in March, down 201,000 bpd from February.
Vienna-based OPEC and its oil producer allies are poised to extend their supply reduction pact into 2019 even as the global glut of crude looks set to be eradicated by September, OPEC Secretary-General Mohammad Barkindo told Reuters.
The International Energy Agency (IEA), which coordinates the energy policies of industrialized nations, signaled on Friday that markets could become too tight if supply remains restrained.
"It is not for us to declare on behalf of the Vienna agreement countries that it is 'mission accomplished', but if our outlook is accurate, it certainly looks very much like it," the IEA said.
Meanwhile, China's March crude oil imports climbed to the second-highest level on record.
U.S. drillers added seven oil rigs in the week to April 13, bringing the total count to 815, the highest since March 2015, General Electric Co's Baker Hughes energy services firm said in its closely followed report on Friday. <RIG-OL-USA-BHI>
(Additional reporting by Stephanie Kelly in New York, Osamu Tsukimori in Tokyo and Shadia Nasralla in London; Editing by Bernadette Baum)