* U.S. crude stocks likely fell 3.5 million barrels - poll
OPEC oil output falls in Nov to lowest since May - survey
* API supply report due at 2130 GMT (Updates prices, adds quote, previous SEOUL)
By Alex Lawler
LONDON, Dec 5 (Reuters) - Oil steadied above $62 a barrel on Tuesday as expectations of a drop in U.S. crude inventories and prolonged supply curbs by OPEC and other producers countered rising output in the United States.
An OPEC-led producer group last week extended a supply-cutting deal through 2018, but the resulting support for prices could bolster U.S. output which climbed to nearly 9.5 million barrels per day in September.
Brent crude, the global benchmark, was down 11 cents at $62.34 a barrel by 0950 GMT. U.S. crude, known as West Texas Intermediate, was down 20 cents at $57.27.
"U.S. output will play the most significant role on the supply front in 2018," said Tamas Varga of oil broker PVM.
"A jump above $60 in WTI could easily push U.S. production over the 10 million bpd mark, increasing the non-OPEC forecast and capping further attempts to push prices higher."
The Organization of the Petroleum Exporting Countries, Russia and other non-OPEC producers last week extended their deal to cut output by 1.8 million barrels per day (bpd) until the end of 2018.
OPEC and its allies are trying to get rid of excess oil in storage. They have made progress in this task and the latest U.S. inventory reports are likely to show a third straight weekly drop in crude stocks.
Analysts expect the reports from industry group American Petroleum Institute (API) and the government's Energy Information Administration (EIA) to show crude stocks fell by 3.5 million barrels.
The API report is out at 2130 GMT on Tuesday, followed by the government supply report on Wednesday.
OPEC has shown strong compliance with the supply cut pledge and in November output fell by 300,000 bpd to its lowest since May, according to a Reuters survey.
However, rising U.S. oil production presents a headwind for OPEC's efforts and data last week showed U.S. crude output rose to nearly 9.5 million bpd in September, approaching the high of 9.63 million bpd seen in 2015. (Additional Reporting by Jane Chung; Editing by Susan Fenton)