* 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
* Oil cut deal to be reviewed before next June -Kuwait
* UAE says OPEC to next June announce strategy to exit cuts (Adds UAE comment, updates prices)
SINGAPORE, Dec 11 (Reuters) - Oil prices fell on Monday as last week's rise in the U.S. rig count pointed to a further increase in American production that could undermine OPEC-led efforts to tighten markets.
A statement by Kuwait's oil minister that OPEC and other oil producers will study before June next year the possibility of exiting their global oil supply-cut agreement also weighed on prices, traders said.
U.S. West Texas Intermediate (WTI) crude futures were at $57.25 a barrel at 0629 GMT, down 11 cents, or 0.2 percent, from their last settlement.
Brent crude futures, the international benchmark for oil prices, were down 15 cents, or 0.2 percent, at $63.25 a barrel.
"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.
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>
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 efforts led by the Organization of the Petroleum Exporting Countries (OPEC) and a group of non-OPEC producers, including Russia, to support prices by withholding supplies.
HOW LONG TO CUT?
OPEC and its allies started withholding supplies last January, and a decision was announced in late November to continue doing so throughout 2018.
However, some uncertainty remains over the reliability of this commitment as well as over how suddenly the group will increase output once the voluntary restraint ends.
Kuwait's oil minister Essam al-Marzouq said on Sunday, however, OPEC and other oil producers will study before June possibly ending the global oil supply cuts earlier.
The United Arab Emirates Energy Minister Suhail bin Mohammed al-Mazroui said on Monday that OPEC and non-OPEC oil producers plan to announce an exit strategy from global oil supply cuts next June.
"We will announce ... a strategy in the June meeting, that does not mean we will exit in June. That means we will come up with a strategy," he said in Abu Dhabi. The UAE holds OPEC presidency in 2018.
(Reporting by Henning Gloystein; Editing by Joseph Radford and Kenneth Maxwell)