Crude for February delivery was trading up 82 cents at $36.17 a barrel by 0203 GMT. It settling down 9.3 percent, or $3.63, on Wednesday, not far off the more than 4-½ year low struck a week ago. London Brent crude was up 75 cents at $37.36, after settling down $3.75 on Wednesday.
Markets were closed on Thursday for Christmas Day.
Oil prices have dropped about $110 a barrel since their mid-July peak as the global financial crisis chipped away at fuel demand, spurring OPEC producers to cut 5 percent of global oil production to stem the slide.
The Abu Dhabi National Oil Co (ADNOC), the main producer in the United Arab Emirates, the world's fifth-largest oil exporter, will continue to supply its customers of flagship Murban crude with 15 percent less than normal contractual supplies in January, while Upper Zakum supplies will be reduced by 3 percent from the norm.
ADNOC said it will reduce supplies of all four crude grades for February, the deepest supply cuts since it started cutting allocations in November.
A source with an Asian refiner said the ADNOC cuts were more than expected.
"ADNOC had already allocated January volumes, but they reversed the decision, so that messes up our schedule," the source said. "For February, the reduction volumes are very large, so we may need to adjust our ship loadings."
Analysts and refiners said the notice was hard evidence that one of OPEC's core members was implementing its share of the group's agreed 2.2 million barrel per day (bpd) production cut, giving relief to an oil price that had been undermined by worries about adherence to OPEC's cuts.
Oil tumbled on Wednesday on news that U.S. jobless claims had risen to a 26-year high and consumers had cut spending for the fifth consecutive month in November, reinforcing expectations of a prolonged slowdown in energy consumption.
A U.S. Energy Information Administration report on Wednesday showed crude inventories dropped 3.1 million barrels last week, countering expectations of a 400,000 barrel rise, but dealers said larger-than-expected builds in U.S. refined fuel supplies last week kept the outlook bearish.
OPEC may call an emergency meeting before March if prices extend their slide, President Chakib Khelil said on Tuesday.
Japan's deepening recession is expected to cut oil demand in the world's third-biggest oil consumer by 4.7 percent in the year starting in April, after sliding 5.7 percent in the fiscal year ending next March, the Institute of Energy Economics (IEE), Japan, said in its annual outlook this week.
In yet another sign that lackluster demand was hurting, a company source from China offshore oil specialist CNOOC Ltd said the firm was likely to scale down or delay some projects as slumping oil prices threatened to invalidate its previous oil economics.
