* OPEC extended output curbs at Vienna meeting on Thursday
* Shows "strong commitment" to balanced market - Goldman
* OPEC deal to be reviewed in June
* Upcoming: U.S. oil rig count by Baker Hughes at 1 p.m./1800 GMT (Adds latest prices, fresh quotes)
NEW YORK, Dec 1 (Reuters) - Oil climbed on Friday, approaching its highest level since the summer of 2015 a day after OPEC and other major producers agreed to continue reining in output until the end of 2018 to try to reduce the global oil glut and boost prices.
The Organization of the Petroleum Exporting Countries and some non-OPEC producers led by Russia agreed on Thursday to keep current limits on output in place until the end of next year, although they signaled a possible early exit from the deal should the market overheat and prices rise too far.
Brent futures were trading at $64.17 a barrel by 10:51 a.m. EST (1551 GMT), with the new front month February up 60 cents, or 0.9 percent, from where the January contract expired on Thursday. The lower priced February future, was up about 2.3 percent from where it closed in the previous session.
U.S. West Texas Intermediate crude (WTI) was up $1.33, or 2.3 percent, at $58.73. WTI's January contract does not expire till Dec. 19.
In November, both oil benchmarks traded at their highest levels since June 2015 with Brent hitting $64.65 and WTI at $59.05. They respectively gained 3.5 percent and 5.5 percent in the month.
Despite recent gains, Brent was on track to rise less than 1 percent for the week, while WTI was headed for a decline of less than 1 percent.
"The market is giving the OPEC, non-OPEC accord its due. The Saudi oil minister came across as resolute and determined to see global crude oil inventories reduce," said John Kilduff, partner at energy hedge fund Again Capital LLC in New York.
The deal, which has been in place since January and was due to expire in March, has seen producers reduce output by 1.8 million barrels per day (bpd), helping to halve global oil oversupply over the past year.
It has allowed Brent prices to return above $60 per barrel, recovering from lows of $27 per barrel hit in January 2016.
But the price rise has also revived the specter of the bull market of the last decade when Brent prices soared.
These concerns led Russia to stress the need for clarity on an exit strategy from the deal and to this end, a reference to a review process in June was included.
"It leaves a question mark about the second half (of 2018) and about the commitment of Russian oil companies, which will be price dependent," Petromatrix strategist Olivier Jakob said.
The chief executive of Russia's top private producer Lukoil told Reuters he would like to see the price of oil stable at current levels, trading in the $60-65 per barrel range.
Price rises could also fuel more drilling in the United States, which is not party to the agreement, Russia warned.
Rising U.S. production has been a thorn in OPEC's side, undermining the impact of its output curbs. The market is awaiting U.S. rig count data, an indicator of future production, at around 1 p.m. EST.
U.S. oil production <C-OUT-T-EIA> hit a new record of 9.68 million bpd last week, while on a monthly basis, it rose to its highest since 2015, growing to 9.5 million bpd in September, according to federal energy data going back to 2005. On an annual basis, output peaked at 9.6 million bpd in 1970.
"Countries involved in the (OPEC) deal ... will keep a close eye on U.S. oil production and will not shy away from taking appropriate steps to counter its impact, said Abhishek Kumar, Senior Energy Analyst at Interfax Energys Global Gas Analytics in London.
(Additional reporting by Polina Ivanova in London and Aaron Sheldrick in Tokyo; Editing by Marguerita Choy and David Evans)