Brent crude oil <LCOc1> settled up 44 cents or 0.7 percent at $63.93 a barrel, still close to Tuesday's intra-day high of $64.65, which was the highest since June 2015.
U.S. light crude <CLc1> was up 46 cents or 0.8 percent at $57.27, just shy of this week's more than two-year high of $57.69 a barrel.
"The move is driven by developments in Saudi Arabia in recent days and anticipation that the consolidation of power by King Salman and the Crown Price will continue," said Abhishek Kumar, Senior Energy Analyst at Interfax Energy's Global Gas Analytics in London, "Meanwhile, Saudi comments on Lebanon have also highlighted rising tensions between the kingdom and Iran."
"Growing confidence in the market that the upcoming OPEC meeting will result in an extension to the output-cut agreement is also supporting prices," he said.
Saudi Arabia plans to cut crude exports by 120,000 barrels per day in December from November, slashing allocations to all regions, a spokesman for the energy ministry told Reuters.
Several traders said prices got a boost from unconfirmed rumors that Saudi King Salman would relinquish the throne to his son Crown Prince Mohammed Bin Salman. Similar rumors were spread in September and October.
Prices got a boost this week from a crackdown on corruption by the Saudi crown prince. Still, traders expressed caution that the oil price rally may have run its course after pushing up Brent more than 40 percent since July.
"It doesn't matter how bullish the fundamentals are ... when an asset goes vertical there is always room for a pullback and consolidation of recent price moves," said Greg McKenna, chief market strategist at brokerage AxiTrader.
The rally has largely been driven by crude output cuts from producing nations led by the Organization of the Petroleum Exporting Countries and Russia. OPEC will discuss output at a meeting on Nov. 30, and is expected to extend the limits beyond their expiry in March 2018. If that happens, some said prices could rally more.
"With the OPEC/non-OPEC deal extension beyond March 2018 a certainty, prices may become stronger and temporarily reach the $65-$70 per barrel range in 2018," said energy consultancy FGE.
U.S. crude production <C-OUT-T-EIA> rose 67,000 barrels per day to 9.62 million bpd, the highest for decades, and looked set to rise further. Texas issued 997 oil and gas drilling permits last month, up nearly 17 percent from a year earlier..
Global oil inventories accelerated draws in October on OPEC-led output cut efforts, and total crude inventories dropped around 93 million barrels between July and November, according to analysis firm Kayrros.
(For a graphic on 'U.S. oil production and storage levels' click http://reut.rs/2zHpdcG)
(Additional reporting by Christopher Johnson in London, and Henning Gloystein in Singapore; Editing by Matthew Mpoke Bigg and David Gregorio)
By Julia Simon