* International Energy Agency sees slower oil demand growth
* Brent heads for first weekly drop in five weeks
* Hurricane causes 40 pct drop in Gulf of Mexico oil output
* Coming Up: U.S. rig count data at 1 p.m. EDT/1700 GMT (New throughout, updates prices, market activity and comments; new byline, changes dateline, previously LONDON)
NEW YORK, Oct 12 (Reuters) - Brent crude gave back early gains and turned lower Friday after a closely watched forecaster deemed supply adequate and the outlook for demand weakening, while U.S. crude pared gains but stayed in positive territory on a lift from Wall Street.
The monthly report by the International Energy Agency (IEA) on Friday weighed on crude markets. The IEA said the market looked "adequately supplied for now" and trimmed its forecasts for world oil demand growth this year and next.
"The weaker outlook has gotten a raised profile in the market, but there's potential for a real supply crunch toward the end of this year," said John Kilduff, a partner at Again Capital Management in New York. "The demand outlook is hurt right now because of the situation with the U.S. and China in particular."
International benchmark Brent crude fell 12 cents a barrel to $80.15 by 11:47 a.m. EDT (1547 GMT), after dropping 3.4 percent on Thursday. U.S. crude added 28 cents to $71.25 a barrel.
Both contracts remained headed for the first weekly drop in five weeks, pressured by a big rise in U.S. inventories and fading concerns about shrinking global supplies due to looming U.S. sanctions on Iran's oil exports.
"This is due to a weaker economic outlook, trade concerns, higher oil prices and a revision to Chinese data," said the IEA, which advises industrialised countries on energy policy.
The IEA report is the latest official forecaster to predict weaker demand ahead and conclude that supply is adequate. The Organization of the Petroleum Exporting Countries (OPEC) made a similar move on Thursday.
"The bearish alarm bells are ringing for next year's oil balance as market players brace for the return of a supply surplus," said Stephen Brennock of oil broker PVM.
Early in the session, crude rose as global equities were set for their biggest daily gain in nearly a month. Declining equities amid wider risk-off investor sentiment had pressured oil on Thursday.
"A rebound in equity markets would help Brent to rebound from $80," said Petromatrix analyst Olivier Jakob, adding that a dip below $80 on Thursday did not clearly break that level as a source of technical support.
A drop in U.S. oil production supported prices. In the U.S. Gulf of Mexico, companies cut output by 40 percent on Thursday because of Hurricane Michael, even as some began returning crews to offshore platforms.
Michael made landfall in Florida on Wednesday as the third most powerful hurricane to strike the U.S. mainland, though it has since weakened to a tropical storm.
Oil traders will watch Friday afternoon for the U.S. rig count, an indicator of upcoming production, which is expected at 1 p.m. from Baker Hughes.
(Additional reporting by Aaron Sheldrick and Alex Lawler Editing by David Goodman and David Gregorio)