U.S. West Texas Intermediate (WTI) crude futures CLc1 were at $57.33 a barrel at 0526 GMT, up 17 cents, or 0.3 percent, from their last settlement, Reuters said.
International Brent crude futures LCOc1 were at $63.55 a barrel, up 14 cents, or 0.2 percent.
There has been little price movement in recent trading, with Brent moving within a $63.00 to $63.91 per barrel range since last Friday.
Some upward pressure was taken off after an oil worker strike was called off in Nigeria, traders said.
Despite this, crude has been generally supported by the ongoing Forties pipeline system outage in the North Sea, which provides crude underpinning Brent futures.
"The Forties pipeline closure will continue to put a floor under Brent crude," said Jeffrey Halley of futures brokerage Oanda.
Further price support has been coming from voluntary supply cuts by the Organization of the Petroleum Exporting Countries (OPEC) and a group of non-OPEC producers including Russia.
The cuts were introduced in January and are currently set cover all of next year, but Russia’s Rosneft said on Monday they could be extended beyond 2018.
Read alsoReuters: Oil prices rise, but 2018 outlook points to ample supplyAs a result of the cuts, oil inventories are falling globally.
"OECD industry inventories declined by 40 million barrels in October to 2.92 billion barrels, while global inventories decreased by 61 million barrels to 5.48 billion barrels. This clearly indicates that the market in 4Q17 is in material (1 million barrels per day) supply deficit," Bernstein Energy said.
"Global inventories now stand at less than 56 days (of demand) ... With OPEC's decision to extend cuts, we expect that OECD inventories will reach the 5-year trailing average (2.83 billion barrels) by 3Q18 and long-term average (2.7 billion barrels) by year-end 2018," Bernstein added.
Threatening to undermine the OPEC-led efforts to tighten markets is U.S. crude production C-OUT-T-EIA, which has soared by 16 percent since mid-2016 to 9.8 million bpd, fast approaching that of top producers Russia and Saudi Arabia, which are currently pumping around 11 and 10 million bpd respectively.
U.S. shale production alone is expected to rise by 94,000 bpd in January, marking a 13th consecutive month of increases, the U.S. Energy Information Administration said late on Monday.
Overall, the EIA said it expected U.S. production to hit a record 10.02 million bpd in 2018, on par with Saudi Arabia and not far off top producer Russia, which pumps around 11 million bpd.