* OPEC extended output curbs at Vienna meeting on Thursday
* Shows "strong commitment" to balanced market - Goldman
* OPEC deal to be reviewed in June (Updates prices)
LONDON, Dec 1 (Reuters) - Oil edged up on Friday after OPEC and other major producers agreed to continue reining in output until the end of next year 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 signalled a possible early exit from the deal should the market overheat and prices rise too far.
Brent was trading at $63.17 by 1351 GMT, up 54 cents on the day. U.S. light crude was up 43 cents at $57.82.
"OPEC and the cooperating countries have created a very high level of confidence that they are standing behind the oil market, that they're going to drive the inventories further down," SEB Markets chief commodities analyst Bjarne Schieldrop said.
"They gave a very serious and trustworthy appearance yesterday and that is taking away a lot of the downside in the market," he said.
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 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 spectre 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.
"Without the reference to a June review, Russia would have been tied to the end of 2018; it wanted instead to have an escape clause," Petromatrix strategist Olivier Jakob said.
"It leaves a question mark about the second half 1/8of 2018 3/8 and about the commitment of Russian oil companies, which will be price dependent," he said.
The CEO 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.
The oil market is unlikely to overheat, he added, thanks to cooperation between OPEC and its allies which would allow them to release new output into the market to rebalance it.
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.
U.S. oil production <C-OUT-T-EIA> hit a new record of 9.68 million bpd last week, according to government data released this week.
(Additional reporting by Aaron Sheldrick; Editing by Mark Potter and David Evans)