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UPDATE 3-Oil falls after U.S. drilling picks up

* U.S. drillers add two more rigs

* Rig total at 749, up from 477 a year ago

* Brent holds above $63, WTI drops below $58 (Updates throughout, refreshes prices; adds graphic; changes dateline from TOKYO)

LONDON, Dec 4 (Reuters) - Oil fell on Monday after U.S. shale drillers added more rigs last week, but prices still held close to their highest since mid-2015, supported by an extension to output cuts agreed last week by OPEC and other producers.

Drillers in the United States added two oil rigs in the week to Dec. 1, bringing the total count to 749, the highest since September, energy services company Baker Hughes said in its closely followed report late on Friday. <RIG-OL-USA-BHI>

February Brent crude futures were down 54 cents at $63.19 a barrel by 1003 GMT, while U.S. West Texas Intermediate was down 61 cents at $57.75.

The Brent price hit a two-year high of $64.65 a month ago and has since attracted record investment by fund managers.

The U.S. rig count, an early indicator of future output, has risen sharply from 477 active rigs a year ago after energy companies boosted spending plans for 2017.

Drillers were encouraged during 2017 to increase activity as crude prices started recovering from a multi-year price slump after the Organization of the Petroleum Exporting Countries (OPEC) and some non-OPEC producers, including Russia, agreed to production cuts a year ago.

Last week the producers agreed to extend those cuts of 1.8 million barrels per day (bpd) until the end of next year.

"Market reaction has been positive so far. There are only two worrying aspects ... one is that Iraqs indiscipline has not been discussed, at least not publicly," PVM Oil Associates strategist Tamas Varga said, referring to Iraq's poor compliance with the deal.

"The second is OPECs own forecast for next year. They are by far the most bullish on 2018, with the annual call on their oil at 33.42 million bpd. This compares with the EIA estimate of 32.70 million bpd and IEA prediction of 32.38 million bpd."

The latest agreement allows for producers to exit the deal early if the market overheats. Russian officials had expressed concern that extending the cuts might encourage U.S. shale oil companies, which have been a thorn in OPEC's side, to pump more crude.

U.S. output rose in September to 9.5 million bpd, the highest monthly output since 9.6 million bpd in April 2015, government data shows. On an annual basis, U.S. output peaked at 9.6 million bpd in 1970.

(Additional reporting by Aaron Sheldrick in TOKYO and Emily Chow in KUALA LUMPUR; Editing by David Goodman)