U.S. West Texas Intermediate (WTI) crude futures were at $56.68 a barrel at 0535 GMT, virtually unchanged from their last settlement at $56.69, Reuters said.
Brent crude futures, the international benchmark for oil prices, were steady at $62.20 a barrel.
Read alsoReuters: Oil edges up as U.S. crude stocks fall, but soaring output weighsTraders said a stronger dollar, which has gained 0.9 percent this month against a basket of other leading currencies, was weighing on prices.
A rising greenback attracts financial traders who switch investments between commodity futures and foreign exchange. A strong dollar is also seen by many as a brake on crude prices, as it makes dollar-denominated oil purchases more expensive in countries that use other currencies.
"A strong U.S. dollar could act as a headwind to commodities," Bank of America Merrill Lynch (BoAML) said in its 2018 outlook.
Despite this, China's booming oil demand will this year overtake the United States as the world's biggest crude importer.
China's crude oil imports rose to 37.04 million tonnes in November, or 9.01 million barrels per day (bpd), the second highest on record, data from the General Administration of Customs showed on Friday.
"China's crude oil imports will continue to rise over the coming years, as output declines from several of its giant onshore fields... This will inevitably see China become more reliant on crude oil imports over our forecast period, with import dependency set to increase from a record 68.0 percent in 2017 to nearly 80 percent by 2021," BMI Research said.
Bank of America Merrill Lynch, meanwhile, said healthy global demand and tight supplies should see Brent crude oil rise to $70 per barrel by mid-year.
U.S. investment bank Jefferies said it expects 2018 global oil demand growth of 1.5 million bpd, driven by near 10 percent demand growth in China.
On the supply side, oil prices have been receiving support from the Organization of the Petroleum Exporting Countries (OPEC) and a group of non-OPEC producers, most importantly Russia, which has been withholding supplies to tighten the market.
Largely because of these voluntary production cuts, oil prices rose sharply between June and October, with Brent gaining around 40 percent in value.
Threatening to undermine OPEC's goal to tighten markets is U.S. oil production, which has risen by more than 15 percent since mid-2016 to 9.7 million barrels per day (bpd), the highest level since the early 1970s and close to the output of top producers Russia and Saudi Arabia.
The EIA monthly data on US crude production published November 30 was also somewhat bearish.