International Brent crude oil futures were trading at $54.02 a barrel at 0428 GMT, up 12 cents from their last close, Reuters said.
U.S. West Texas Intermediate (WTI) crude oil futures were at $51.02 per barrel, virtually flat with their last settlement.
ANZ bank said on Thursday that oil markets would move into a substantial deficit in the first quarter of 2017 if the Organization of the Petroleum Exporting Countries (OPEC) and other producers led by Russia go through with their announced cuts of almost 1.8 million barrels per day (bpd) in output.
"This will likely push oil prices well above $60 per barrel early next year," it said.
Crude prices also received some support from falling U.S. crude inventories.
Data from the U.S. Energy Information Administration (EIA) showed that commercial crude inventories last week declined by 2.56 million barrels to 483.19 million barrels.
However, traders said it is far from clear whether OPEC and other producers will follow through with their announced cuts.
OPEC pumped 33.87 million bpd last month, according to figures it collects from secondary sources, up 150,000 bpd from October, OPEC said in a monthly report on Wednesday.
That shows the group's output has continued to rise, adding to a global glut, ahead of the January start of its first supply cut agreement since 2008. That could raise questions about its ability to comply fully with the deal.
Read alsoReuters: OPEC agrees first output cut since 2008, Saudis to take 'big hit'Thursday's more stable prices came after sharp declines late on Wednesday, when crude fell over 3% due to a strong dollar.
The greenback rose to close to 14-year highs against a basket of other currencies as the U.S. Federal Reserve raised rates for the first time in a year.
"The Federal Reserve hike ... saw bond yields rise, dealing a blow to commodities in general," said Jeffrey Halley, senior market analyst at futures brokerage OANDA in Singapore.
A stronger dollar, in which oil is traded, can hit crude demand as it makes fuel purchases more expensive for countries using other currencies at home.