* U.S. Gulf of Mexico oil output halved by Storm Barry
* IEA forecasts global oil surplus
* Iran calls on Britain to release seized tanker
* U.S. oil drillers cut rigs for second week -Baker Hughes (New throughout, updates prices, market activity, adds U.S. rig count, comments)
By Laila Kearney
NEW YORK, July 12 (Reuters) - Oil prices inched up on Friday as U.S. Gulf of Mexico crude output was halved by disruptions caused by a tropical storm, but concerns over a global crude surplus in the months ahead limited gains.
Brent crude futures were up 31 cents to $66.83 a barrel by 1:21 p.m. EDT (1721 GMT). U.S. West Texas Intermediate (WTI) crude futures gained 18 cents to $60.38 a barrel.
Brent has climbed 4% so far this week while WTI was on track for a 5% rise. Both registered declines last week.
Tropical Storm Barry, which is expected to become a hurricane just before making landfall this weekend, boosted crude futures as oil companies in the Gulf of Mexico sliced production.
"The crude oil market is being supported by the Gulf of Mexico production shut-in... it is going to look to see if Tropical Storm Barry becomes a major flooding event that impacts the refining sector in Louisiana and impacts gas and diesel," said Andy Lipow, president of Lipow Oil Associates in Houston.
Companies cut more than 1 million barrels per day (bpd) of output, or 53% of the region's production, as the storm headed for possible landfall on the Louisiana coast on Saturday.
The International Energy Agency (IEA) forecast surging U.S. oil output will outpace sluggish global demand and lead to a large inventory build around the world in the next nine months.
The world energy watchdog's report came a day after the Organization of the Petroleum Exporting Countries predicted a crude glut next year despite an OPEC-led pact to restrain supplies.
"The IEA report laid bare what the market is staring down and what OPEC is staring down next year, and really for the balance for this year, and that will continue to be a headwind," said John Kilduff, a partner at Again Capital LLC in New York.
The weekly U.S. oil rig count, an indicator of future production, fell for the second straight week, General Electric Co's Baker Hughes energy services firm said. Drillers cut four oil rigs in the week to July 12, reducing the total to 784, the lowest since February 2018.
The market remained on edge as tensions intensified between Iran and the West. Tehran on Friday said Britain was playing a "dangerous game" after last week's seizure of an Iranian tanker on suspicion it was breaking European sanctions by taking oil to Syria.
"Only time will tell whether this turns out to be a case of wishful thinking but one thing is clear: geopolitical risks are here to stay," said Stephen Brennock, analyst at PVM Oil Associates.
Additional reporting by Borzorgmehr Sharafedin in LONDON, Jane Chung in SEOUL and Koustav Samanta in SINGAPORE Editing by David Goodman, Marguerita Choy and David Gregorio