* U.S. factory activity sinks to 10-year low in September
* OPEC output drops to lowest in 8 years in Sept -survey
* U.S. oil production falls for 3rd month in July -EIA
* Russia output falls but still above quota
* U.S. crude stockpiles likely rose last week -poll
* Coming Up: API's US oil inventory data at 4:30 p.m.ET/2030 GMT (New throughout, updates prices, market activity and comments, new byline, changes dateline, previous LONDON)
NEW YORK, Oct 1 (Reuters) - Oil prices steadied on Tuesday, pressured by weak U.S. economic data that dimmed the crude demand outlook, while finding some support from reports of an output decline from the world's largest oil producers in the third quarter.
Brent crude futures rose 8 cents to $59.33 a barrel by 11:31 a.m. EDT (1531 GMT), while U.S. West Texas Intermediate crude fell 9 cents to $53.98 a barrel.
Both benchmarks posted their largest quarterly falls this year on Monday, hurt by a slowdown in global economic growth amid the U.S.-China trade war.
U.S. manufacturing activity tumbled to a more than 10-year low in September as the trade tensions weighed on exports, according to a survey from the Institute for Supply Management (ISM). The ISM's forward-looking new orders sub-index, however, edged up to a reading of 47.3 last month from 47.2.
"Oil is still holding positive on the day probably because the manufacturing component and the new orders component seemed to be a little bit more positive looking forward and the drop in manufacturing might be looking backward," said Phil Flynn, an analyst with Price Futures Group in Chicago.
"Still, it was a very disappointing number overall and that's why oil prices gave up their earlier gains."
Oil prices are likely to remain steady, with Brent averaging $65.19 a barrel and WTI $57.96 in 2019, as flagging demand outweighs supply shocks, a Reuters survey showed.
Crude production from the Organization of the Petroleum Exporting Countries fell to the lowest in eight years in September at 28.9 million bpd, down 750,000 bpd from August's revised figure and the lowest monthly total since 2011, a Reuters survey found.
Output at the world's two largest producers, the United States and Russia, also fell in July and September respectively.
Russia's output declined to 11.24 million bpd in Sept. 1-29, down from 11.29 million bpd in the previous month, sources said, although it is still above the quotas set in an output deal between Russia and OPEC.
U.S. crude oil output fell 276,000 bpd in July to 11.81 million bpd as federal offshore Gulf of Mexico production slid, according to a U.S. Energy Information Administration monthly report released on Monday.
U.S. production peaked at 12.12 million bpd in April.
News that Saudi Aramco has restored full oil production and capacity to the levels they were at before attacks on its facilities on Sept. 14 weighed on oil prices on Monday. Saudi Arabia pumped about 9.78 million barrels per day (bpd) in August.
Meanwhile, U.S. crude oil stockpiles likely rose 1.1 million barrels last week, a preliminary Reuters poll showed on Monday, ahead of weekly data. The American Petroleum Institute (API) will release its data at 4:30 p.m. EDT (2030 GMT) on Tuesday, followed by the EIA's report at 10:30 a.m. EDT on Wednesday.
(Additional reporting by Ahmad Ghaddar in LONDON, Florence Tan in SINGAPORE; Editing by Marguerita Choy and Jason Neely)