* U.S. drillers cut for first time in 7 weeks -Baker Hughes
* But U.S. output still expected to rise this year (Re-casts with lower prices)
SINGAPORE, March 12 (Reuters) - Oil prices gave up earlier gains on Monday as rising U.S. output loomed over markets, despite a slowdown in rig drilling activity.
U.S. West Texas Intermediate (WTI) crude futures were at $61.90 a barrel at 0714 GMT, down 14 cents, or 0.2 percent.
Brent crude futures were at $65.36 per barrel, down 13 cents, or 0.2 percent, from their previous close.
Prices had risen on Friday and earlier on Monday.
"A falling rig count and the strong employment data may have helped support prices," said William O'Loughlin, investment analyst at Rivkin Securities.
The U.S. economy added the biggest number of jobs in more than 1-1/2 years in February, with non-farm payrolls jumping by 313,000 jobs last month, the Labor Department said on Friday.
In oil markets, U.S. energy companies last week cut oil rigs for the first time in almost two months <RIG-OL-USA-BHI>, with drillers cutting back four rigs, to 796, Baker Hughes energy services firm said on Friday.
Despite the lower rig count, which is an early indicator of future output, activity remains much higher than a year ago when, when just 617 rigs were active, and most analysts expect U.S. crude oil production <C-OUT-T-EIA>, which has already risen by over a fifth since mid-2016, to 10.37 million barrels per day (bpd), to rise further.
That's more than top exporter Saudi Arabia produces and almost as much as Russia pumps out, at nearly 11 million bpd.
Singapore-based brokerage Phillip Futures said that the oil market "will focus on OPEC and IEA (monthly) reports this week for a sensing on global demand/supply levels for crude oil" and that "items in focus will include OECD commercial stock levels, revision in global demand and supply for crude oil and OPEC's compliance on production levels".
The Organization of the Petroleum Exporting Countries (OPEC), together with a group of other producers led by Russia, has been withholding production since the start of 2017 to prop up prices.
It is not clear when the deal to withhold output will end, but Iranian oil minister Bijan Zanganeh said OPEC could agree in June to begin easing current oil production curbs in 2019, the Wall Street Journal reported on Sunday. 1/8nD5N1N5024
(Reporting by Henning Gloystein Editing by Joseph Radford)