* U.S. oil rig count rises 9 to 738 in week - Baker Hughes
* Strong demand and OPEC-led supply cuts support market
* Hezbollah says Saudi Arabia declared war on Lebanon
* Oil demand strong in southeast Asia (Adds settlement price)
By Scott DiSavino
NEW YORK, Nov 10 (Reuters) - Crude was down slightly on Friday as expectations that OPEC and other producers will extend their production cut agreement were offset by U.S. drillers adding the most oil rigs in a week since June, indicating output will continue to grow.
U.S. energy companies added nine oil drilling rigs this week, the second increase in three weeks, bringing the total count up to 738, General Electric Co's Baker Hughes energy services firm said in its closely followed report. RIG-OL-USA-BHI
Brent futures fell 41 cents, or 0.6 percent, to $63.52 a barrel, while U.S. West Texas Intermediate crude settled down 43 cents at $56.74 per barrel.
Earlier in the week, Brent rose to $64.65, its highest since June 2015, and WTI hit $57.92, its highest since July 2015.
Both contracts were rose more than 2 percent this week, which was the fifth consecutive increase.
Traders said higher prices in recent weeks were the result of efforts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia to tighten the market by cutting output, as well as strong demand and rising political tensions.
There are also expectations in the market that OPEC's next meeting on Nov. 30 will agree to extend cuts beyond the current expiry date in March 2018.
"Market participants expect OPEC to extend the production cuts beyond March 2018 and stocks to decline further," analysts at Commerzbank said, noting, however, that "the higher price level should lead to a further rise in U.S. shale oil production."
U.S. production was forecast to rise to 9.2 million barrels per day (bpd) in 2017 and a record 10.0 million bpd in 2018 from 8.9 million bpd in 2016, according to federal energy projections this week. Output peaked at 9.6 million bpd in 1970.
Goldman Sachs also warned of greater price volatility ahead, citing rising tensions in the Middle East, especially between OPEC members Saudi Arabia and Iran, along with soaring U.S. oil production.
Hezbollah's leader said Saudi Arabia had declared war on Lebanon and his Iran-backed group, accusing Riyadh of detaining Saad al-Hariri and forcing him to resign as Lebanon's prime minister to destabilise the country.
"The political situation in Saudi Arabia remains sufficiently volatile to spike crude values by at least 50 cents at any given time as was the case (Thursday)," Jim Ritterbusch, president of Chicago-based energy advisory firm Ritterbusch & Associates, said in a report, noting he did not expect Friday's oil rig count to exert much price impact.
Another factor supporting prices was strong demand in southeast Asia, where the number of tankers holding oil in storage around Singapore and Malaysia has halved since June.
Additional reporting by Nina Chestney in London and Henning Gloystein in Singapore and Jessica Resnick-Ault in New York; Editing by David Goodman and Marguerita Choy