UPDATE 6-Oil edges further above $62, helped by expected fall in US stocks

* 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 paragraph 4)

LONDON, Dec 5 (Reuters) - Oil edged further above $62 a barrel on Tuesday, supported by strong demand, expectations of a drop in U.S. crude inventories and an OPEC-led deal to extend oil output cuts.

Concerns that the OPEC-led producer group's Nov. 30 decision to prolong their supply-cutting deal through 2018 could bolster U.S. shale drilling limited gains, however. U.S. production climbed to nearly 9.5 million barrels per day in September.

Brent crude, the global benchmark, was up 25 cents at $62.70 a barrel by 1443 GMT. U.S. crude, known as West Texas Intermediate, rose 3 cents at $57.50.

"Demand remains firm which is the main reason for us to still see oil at above $60 per barrel," said Georgi Slavov, head of research at Marex Spectron.

The Organization of the Petroleum Exporting Countries, Russia and other non-OPEC producers last week extended the deal to cut output by 1.8 million barrels per day (bpd) until the end of 2018 to get rid of excess oil in storage.

Faster-than-expected growth in demand this year has given tailwind to OPEC's efforts to clear the glut 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.

"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." (Additional Reporting by Jane Chung; Editing by Susan Fenton)