UPDATE 9-Oil falls more than 1 pct down on OPEC deal uncertainty

* Unclear path for OPEC cuts unsettles market

* OPEC, non-OPEC committee recommends extending cuts by 9 months

* Potential review clause in OPEC deal could shorten extension

* U.S. crude stocks fall, fuel builds more than forecast -EIA (Adds quote, comment, updates prices)

NEW YORK, Nov 29 (Reuters) - Oil prices hit session lows on Wednesday in a volatile session buffeted by conflicting statements from oil ministers a day ahead of OPEC's meeting in Vienna, as members debate the path for an extension of the group's supply-cut agreement.

Brent crude futures fell 82 cents to $62.79 a barrel as of 12:57 p.m. EST (1757 GMT), while U.S. crude fell 97 cents to $57.01 a barrel.

The oil market has pulled back over the last two days on concerns that the Organization of Petroleum Exporting Countries, and key non-members like Russia, might consider only a short-term extension to its current deal cutting supply by 1.8 million barrels per day (bpd) till March.

That uncertainty carried through to Wednesday, which some analysts attributed to the market's generally positive tone in recent weeks in anticipation of an extension to the supply-cut deal.

"The output cut agreement might be largely priced in by now and once they announce it, the market is going to be looking to what's next," said Gene McGillian, manager of market research at Tradition Energy in Stamford, Connecticut.

The market was less affected by a larger-than-expected 3.4 million-barrel drawdown in U.S. crude inventories, although gasoline and distillate stocks rising more than anticipated weighed.

Crude futures hit a session high after Kuwait's Oil Minister Essam al-Marzouq said a key monitoring committee recommended extending the group's supply-cut agreement through the end of 2018, but those sentiments were undercut by statements from Russia's oil minister, who suggested the oil market still has yet to balance.

The cartel is still weighing the offsetting factor of rising U.S. production, and considering a clause that would allow the group to review a potential extension at its spring 2018 meeting in May or June.

"There is growing anticipation of the output-cut agreement being extended for the rest of 2018; however, possibility for a review clause will be closely looked at," said Abhishek Kumar, senior energy analyst at Interfax Energys Global Gas Analytics in London.

Reluctance to agree a lengthy extension has been driven mainly by Russia and its concerns that a major extension could lead the market to overheat.

Moscow fears a strong price rally off the back of such a move could give an unsustainable boost to the rouble, one that harms Russian exports.

Some Russian producers including Rosneft, run by an ally of President Vladimir Putin, Igor Sechin, have questioned the rationale of prolonging the cuts, saying it will lead to a loss of market share to U.S. producers, which are not reducing output.

U.S. production has been hitting records on a weekly basis in recent months, and for the week to Nov. 24, production rose to 9.68 million bpd. That is still short of the 10 million-plus bpd record set in the early 1970s, per monthly data from the U.S. Energy Information Administration.

The drawdown in U.S. crude was driven by the shutdown of the Keystone pipeline, which cut inventories at the Cushing, Oklahoma oil hub by 2.9 million barrels, the largest weekly drawdown in eight years. The 590,000-bpd line was restarted on Tuesday.

U.S. gasoline and distillate stocks rose more than expected, however, in part due to weak implied gasoline demand, which fell to a five-year seasonal low in the most recent week.

The steady rise in production may continue to boost U.S. exports, which will compete with OPEC's market share around the world.

Overall net imports into the United States fell to 5.9 million bpd in the most recent week, down from 7.1 million bpd at this time a year ago. (Additional reporting by Henning Gloystein and Polina Ivanova; Editing by Marguerita Choy and Mark Potter)