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UPDATE 4-Oil prices fall as Russia touts easing OPEC+ output

Ron Bousso

* Russia says OPEC+ may consider easing output cuts

* Kuwait-Saudi Neutral Zone dispute nears resolution

* Hopes of U.S.-China trade deal support prices

* U.S. oil rigs count rises most since February 2018

* Graphic on U.S. rig count: https://tmsnrt.rs/2XdttIW (Adds Neutral Zone, Russian energy minister, updates prices)

LONDON, Dec 23 (Reuters) - Oil fell on Monday after Russia said an OPEC-led pact may consider easing output cuts next year but prices held near recent three-month highs on hopes for a trade deal between the United States and China.

Brent crude was down 19 cents, or 0.29%, at $65.95 per barrel by 1010 GMT in thin trading ahead of the Christmas holiday. West Texas Intermediate was down 29 cents, or 0.48%, at $60.15 a barrel.

The Organization of the Petroleum Exporting Countries and other top producing nations led by Russia agreed this month to extend and deepen output cuts in the first quarter of 2020.

However, Russian Energy Minister Alexander Novak said on Monday that the group known as OPEC+ may consider easing the output restrictions at their meeting in March.

"We can consider any options, including gradual easing of quotas, including continuation of the deal," Novak told Russia's RBC TV in an interview recorded last week, adding that Russia's oil output was set to hit a record high this year.

Non-OPEC global supply is expected to rise next year due to higher output from countries including the United States, Brazil, Norway and Guyana, which became an oil producer last week.

Another source of more oil could emerge in the coming months after Kuwait indicated that a long-standing dispute over the "Neutral Zone" on its border with Saudi Arabia will resolve by the end of 2019.

Production at two large oil fields in the Neutral Zone was halted more than three years ago, cutting output by some 500,000 barrels per day.

Oil prices have risen since the United States and China agreed a so-called phase one trade deal earlier this month following months of tit-for-tat negotiations that unsettled markets.

Under a deal due to be signed in January, the United States is expected to agree to reduce some tariffs in return for a big increase in purchases U.S. agricultural products by Chinese importers.

"Oil prices will continue to benefit from the positive developments in U.S.-China trade," said Stephen Innes, chief Asia market strategist at AxiTrader.

Data showing that U.S. energy companies added the most oil rigs last week since February 2018, primarily in the Permian shale basin, also put pressure on prices.

Although the oil rig count was on track to fall for the first year since 2016 as drillers slash spending to focus on returns, higher productivity means that output in most shale basins has increased to record levels this year.

(Additional reporting by Aaron Sheldrick in Tokyo; editing by Richard Pullin, Jason Neely and David Clarke)