Brent crude futures were down 26 cents a barrel at $63.27 a barrel by 12:22 p.m. EST (1722 GMT), after touching a low of $62.61 a barrel. US West Texas Intermediate (WTI) crude futures were flat at $56.74 after dipping earlier to $56.30.
Middle East tensions have supported the market, despite concerns that output could rise further.
"The rise by Saudi Arabia to produce more than 10 million barrels per day would have registered more," said John Kilduff Partner at Again Capital. "This is a new level of geopolitical risk," he said. Additionally, the market has less supply overhang than it did a year ago, he said.
On the supply side, tensions in the Middle East raised the prospect of disruptions, traders said. A purge this month of Saudi Arabia's leadership by Crown Prince Mohammed bin Salman is one of the key factors raising concerns about political stability of the region's largest oil producer.
Other regional concerns include war in Yemen and growing tensions between Saudi Arabia and Iran is a concern to investors too.
Additionally, traders said it was unclear whether a strong earthquake that hit Iran and Iraq on Sunday had affected the region's oil production.
Bahrain said at the weekend that an explosion that caused a fire at its main oil pipeline on Friday was caused by sabotage, linking the attack to Iran, which denied any role.
Traders said crude prices were well supported as output cuts led by the Organization of the Petroleum Exporting Countries and Russia have contributed to a reduction in excess supply that had dogged markets since 2014.
OPEC forecast higher demand for its oil in 2018 and said its production-cutting deal with rival producers was reducing excess oil in storage, pointing to an even tighter global market next year. However, it also pointed out that Saudi output had risen above 10 million barrels per day.
The level of inventories held by industrialised above the five-year average "has fallen by more than 50 percent in 2017, with inventories currently at around 160 million barrels," consultancy Timera Energy said.
"If current trends continue, inventories are likely to return to the five-year average at some stage in 2018," it said, adding that strong demand had also helped reduce the glut.
OPEC has sought to push stocks to the five-year average.
Hedge funds increased holdings of Brent futures and options in the latest week, extending their bet on a rally to the highest on record. Managers now hold net long positions equivalent to nearly 544 million barrels of oil.
"Overall, there are a few reasons for confidence - compliance from OPEC - and it seems likely they'll extend the cut," said Jasper Lawler, a market strategist at London Capital Group, referring to the output deal due to expire in March.
US producers added nine oil rigs last week, the biggest jump since June, raising the count to 738, energy services firm Baker Hughes said on Friday.
The rig count fell in August, September and October, but last week's rise was the second in three weeks, indicating that the US oil industry was comfortable operating at current prices.