* Brent and WTI ease after Monday surge
* Saudi crown prince cements hold on power
* Tensions rise with Iran over Yemen conflict
* EIA raises U.S. oil output growth forecast for 2018
* Coming up: Weekly API U.S. oil data at 4:30 p.m. EDT (Updates prices, adds EIA reports, quotes; changes byline, changes dateline from London)
NEW YORK, Nov 7 (Reuters) - Oil eased on Tuesday after rising to the highest since July 2015 the previous day, while tension flared between Saudi Arabia and Iran and the Saudi crown prince tightened his grip on power.
Brent crude futures were down 51 cents, or 0.8 percent, at $63.76 a barrel by 12:32 p.m. (1732 GMT), having climbed 3.5 percent on Monday.
U.S. West Texas Intermediate (WTI) crude was down 20 cents, or 0.3 percent, to $57.15 a barrel.
Saudi Crown Prince Mohammed bin Salman moved to shore up his power base with the arrest of royals, ministers and investors, which an official described as part of "phase one" of a crackdown.
More tellingly, tensions escalated between OPEC members Saudi Arabia and Iran, which analysts said did more to rattle the market than the prince's purge.
"Saudi Arabia is really going all-in again against Iran and that is, for me, more the focus than the domestic issue," Petromatrix strategist Olivier Jakob said.
"On the one hand, it increases the global geopolitical risk level, but it also increases the difficulty of keeping consensus within OPEC."
The Organization of the Petroleum Exporting Countries, led by Saudi Arabia, has agreed to restrain crude output by 1.8 million barrels per day (bpd) together with 10 other nations including Russia until March 2018.
OPEC meets at the end of this month and has been widely expected to extend the deal.
The producers are in the process of inviting other countries to the Nov. 30 meeting, OPEC's Mohammad Barkindo told reporters on Tuesday, with a view to joining the deal. He declined to name the countries concerned.
Brazil has rejected an informal effort by Saudi Arabia to coax Latin America's top oil producer into joining OPEC-led production cuts aimed at boosting prices that have been hit by oversupply, a Brazilian official said.
The Saudi-led coalition fighting against the Houthi movement in Yemen said on Monday that it was closing all Yemeni air, sea and land crossings after a missile was fired towards Riyadh at the weekend.
Saudi Arabia and its Gulf allies have said they see Iran as responsible for the Yemen conflict and on Monday Saudi Foreign Minister Adel al-Jubeir said his country reserves the right to respond to Iran's "hostile actions."
The U.S. Energy Information Administration said it forecast domestic crude oil production in 2018 to rise by more than previously expected.
In its monthly short-term energy outlook, the agency forecast that U.S. crude oil output will rise by 720,000 barrels per day (bpd) to 9.95 million bpd in 2018. Last month, it expected a 680,000 bpd year-over-year increase to 9.92 million bpd.
Market watchers were looking ahead to weekly energy data from the American Petroleum Institute at 4:30 p.m. EDT (2030 GMT), which was forecast to show a drawdown in crude and product inventories for last week.
"Today we get the API... and the market will need to see supportive fundamentals," said Gene McGillian, director of market research at Tradition Energy in Stamford, Connecticut.
(Additional reporting by Amanda Cooper in London, Jane Chung in Seoul and Aaron Sheldrick in Tokyo; Editing by Marguerita Choyand David Goodman)