* Strong demand, OPEC-lead supply cuts support market
* Middle East tensions could cause volatility
* Rising U.S. output may weigh on prices
SINGAPORE, Nov 10 (Reuters) - Oil markets were stable on Friday, supported by ongoing supply cuts led by OPEC and Russia as well as by strong demand, although the prospect of rising U.S. shale output capped prices around recent gains.
Brent crude futures were at $63.84 per barrel at 0120 GMT, down 9 cents from their last close, but still near a more than two-year high of $64.65 a barrel reached earlier this week.
U.S. West Texas Intermediate (WTI) crude was at $57.05 per barrel, down 12 cents but also still close to this week's more than two-year peak of $57.92 a barrel.
Analysts said that the high prices were a result of efforts by the Organization of the Petroleum Exporting Countries (OPEC) and Russia to withhold supplies to tighten the market, as well as strong demand and rising political tensions.
"Oil prices have rallied sharply over the past week ... The latest catalyst for this move higher was the sharp rise in geopolitical tensions last weekend, with growing confidence in an OPEC extension and strong oil demand fueling the rally previously," said U.S. bank Goldman Sachs.
Goldman warned of greater price volatility ahead due to increasing tensions in the Middle East, especially between OPEC fellows but political arch-rivals Saudi Arabia and Iran, along with soaring U.S. oil production.
"We see potential for high spot price volatility in the coming weeks," Goldman said.
"A rise in the U.S. rig count and a non-committal OPEC meeting would push prices lower, in our view, yet additional escalation of recent geopolitical tensions could lead to another large rally," it added.
ANZ bank said that "political stability was jolted awake this week" in the Middle East.
"While the likelihood of a disruption to (oil) supply remains low, we believe the events raise the probability of Saudi Arabia taking a more aggressive stance on production curbs. In fact, the risks now lie towards curbs remaining in place longer than expected. As such, we see oil prices remaining well supported in the short term," ANZ said.
OPEC is due to discuss output policy during a meeting on Nov. 30, and it is expected the group will extend the cuts beyond the current expiry date in March 2018.
"Recent OPEC communication suggests that an extension will be announced but there are no details on volumes," Goldman said. (Reporting by Henning Gloystein; Editing by Joseph Radford)