* U.S. rig count up to 751, highest since Sept -Baker Hughes
* U.S. oil production heads for 10 million bpd
* Output rise undermines OPEC-led efforts to tighten market (Updates throughout, changes dateline from SINGAPORE)
LONDON, Dec 11 (Reuters) - Oil markets edged lower on Monday as ongoing output cuts led by OPEC were countered by rising U.S. drilling activity that points to a further increase in American production.
Brent crude futures, the international benchmark for oil prices, were 15 cents lower at $63.25 a barrel at 0950 GMT.
U.S. West Texas Intermediate (WTI) crude futures were at $57.03 a barrel, down 33 cents from their last settlement.
Both Brent and WTI crude oil settled more than 1 percent higher on Friday, and oil prices have gained well over a third in value from their 2017 lows.
"It's time for a breather," said Warren Patterson, commodities strategist with ING.
The gains are largely due to production cuts by the Organization of the Petroleum Exporting Countries and a group of non-OPEC producers, including Russia, which have been in place since the start of the year.
But analysts said the effect of these cuts could be undermined by rising output from the United States, which is not participating in the deal to voluntarily withhold production.
The number of rigs drilling for new oil output in the United States rose by two in the week to Dec. 8, to 751, the highest level since September, General Electric Co's Baker Hughes energy services firm said on Friday. <RIG-OL-USA-BHI>
"The largest concern for investors currently remains the rise in the U.S. rig count, which could potentially jeopardize the OPEC and Russian agreement when they meet for a review in June 2018," said Shane Chanel, equities and derivatives adviser at ASR Wealth Advisers.
A higher rig count points to a further rise in U.S. crude production <C-OUT-T-EIA>, which is already up by more than 15 percent since mid-2016 to 9.71 million barrels per day (bpd).
That's the highest level since the early 1970s, and close to levels from top producers Russia and Saudi Arabia.
Rising U.S. output threatens to undermine the OPEC-led supply cuts. The group started withholding supplies last January, and announced in late November that they would continue doing so throughout 2018.
But Kuwait's oil minister said on Sunday that OPEC and other oil producers will study before June the possibility of an exit strategy from the oil supply-cut agreement.
Meanwhile, The United Arab Emirates energy minister Suhail said on Monday that OPEC and non-OPEC oil producers plan to announce in June an exit strategy from the cuts.
(Additional reporting by Henning Gloystein in Singapore, editing by David Evans)