Crude futures were poised for their first weekly gain this year, but analysts said there had been no shift in the fundamental backdrop of supply far exceeding demand and swelling inventories of unwanted oil and oil products.
The oil price is set for a 16.8% fall in January, its largest slide in the first month of the year in at least a quarter century.
"There is no fundamental justification whatsoever to think that the current downtrend is changing," said PVM Oil Associates analyst Tamas Varga.
"All one has to do is look at this month's report from the IEA to see that, especially the first half of this year, the market is going to be oversupplied," he said, referring to a report by the Paris-based International Energy Agency.
Brent was up $1.92 at $31.17 a barrel by 1200 GMT, off this week's 2003 low of $27.10 and heading for a more than 6% weekly gain, while U.S. crude rose $1.59 to $31.12.
In its monthly report on Tuesday, the IEA said oil supply would outpace demand for at least another year and the oil market risked "drowning in oversupply".
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That said, this week traders have bought a raft of derivatives giving them the option to buy oil at $40 a barrel by December, suggesting that the worst of the rout may be over for now.
Freezing weather conditions and snowstorms have gripped the U.S. East Coast and parts of continental Europe, feeding demand for heating oil and helping to boost oil.
Threatening oil's ability to build on its gains was the comparatively mild rally that took place in the longer-dated Brent futures contracts.
Prices for oil for delivery in one year's time rose by a mere 2% on the day, compared to the near-7% rise in prices for prompt delivery, narrowing the difference, or contango, between the two.
"This is not a sustainable rally given the current surplus either the longer-dated contracts need to be lifted along with the front-end rally or the front-end rally needs to fade and fall back," SEB analyst Bjarne Schieldrop said in a note.