* US crude stocks up, products draw down - EIA
* IEA cuts demand outlook, contrasts with OPEC, EIA (Rewrites throughout, updates with settlement prices, quote)
By Gabriel Debenedetti
NEW YORK, Feb 13 (Reuters) - Brent crude oil prices rose slightly on Wednesday to close near $119 a barrel and remain close to a nine-month high, though gains were capped by a rise in U.S. crude oil inventories and as the International Energy Agency (IEA) trimmed its demand outlook.
The rise in inventories in the world's largest oil consumer weighed on U.S. crude oil prices, which closed lower and just above $97 a barrel, down more than $1 from the day's peak.
The U.S. Energy Information Administration said crude stocks rose by 560,000 barrels in the week ending Feb. 8, though the gain was slightly less than expected by analysts, while stockpiles of gasoline and distillates fell, according to its weekly report.
"The underlying supply and demand fundamental picture really hasn't changed. We have a lot of oil here in the United States," said Gene McGillian, analyst at Tradition Energy in Stamford, Connecticut.
March Brent futures settled 6 cents up at $118.72 a barrel, having earlier touched a session high of $119.12. The March Brent futures contract expires today. The April contract finished up 13 cents at $117.88.
U.S. crude futures, which finished lower last week for the first time in nine weeks, were down 50 cents at $97.01.
After narrowing in early trade, Brent's premium over U.S. crude eventually widened to $22.11 a barrel. Brokers pointed to technical resistance at the spread's 100-day moving average around $20.68 as one reason for the reversal during Wednesday's trading.
Brent was also supported by positive economic data as a Reuters poll showed that the euro zone is slowly starting to emerge from recession.
While Brent has risen by almost $10 a barrel since the middle of January, boosted by signs of strong demand from China and Saudi output cuts, the IEA on Wednesday said that the slow pace of economic recovery would keep consumption in check.
In its monthly report, the agency trimmed its demand growth forecast for 2013 by 90,000 barrels per day. That was in contrast to both the EIA and the Organization of the Petroleum Exporting Countries (OPEC), which both raised their demand growth forecasts on Tuesday.
Prices were supported by the IEA report on Wednesday stating that Iranian oil exports will likely fall further this year as the West tightens sanctions on Tehran. Exports from Iran have already fallen to the lowest level in 30 years, the IEA said.
Additional reporting by David Sheppard and Robert Gibbons in New York, Simon Falush and Dasha Afanasieva in London; Editing by William Hardy and Bob Burgdorfer