International Brent crude oil futures were trading at $53.93 a barrel at 0649 GMT, up 3 cents from their last close.
According to Reuters, U.S. West Texas Intermediate (WTI) crude oil futures were at $50.96 per barrel, down 8 cents from their last settlement.
"This will likely push oil prices well above $60 per barrel early next year," it said.
Although traders said it remained unclear whether OPEC and other producers will follow through with their announced cuts, a tighter market will also be the result of years of falling investment into new production, as operators slashed costs in order to survive the low price environment.
"2017 will be the third year investments go down, with 3 percent (declines). You need to go back to the 80s to see three consecutive years of investment cuts," said Audun Martinsen, Vice President for Oilfield Service Research at Rystad Energy.
In the near term, crude received support from falling U.S. crude inventories.
U.S. Energy Information Administration (EIA) data showed that commercial crude inventories last week declined by 2.56 million barrels to 483.19 million barrels.
Thursday's more stable prices came after sharp declines late on Wednesday, when crude fell over 3 percent 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.