Brent crude rose 45 cents, or 0.8pc, to $59.96 a barrel by 1150 GMT. U.S. crude was up 33 cents, or 0.6pc, at $53.81.
Financial markets that have been hit by the spread of the virus out of China are trying to assess the economic fallout, with the death toll rising to 132 and airlines reducing flights to China.
"While the coronavirus continues to spread both in and outside China the market is trying to adjust positions across all asset classes," said Saxo Bank analyst Ole Hansen.
"Commodities, most of which depend on global growth and demand, have been caught in the crosshairs of these developments ... China (is) the world's biggest buyer of most commodities, from crude oil and fuel to copper and iron ore."
British Airways suspended all direct flights to and from mainland China after Britain warned against all but essential travel to the country, and jet fuel demand has slumped in Asia as airlines have cancelled connections.
The Organization of Petroleum Exporting Countries (OPEC) wants to extend oil production cuts until at least June, from March, and could deepen the reductions should demand for oil in China be significantly reduced by the spread of the virus, OPEC sources said.
OPEC and its allies, including Russia, have been trying to stabilise prices amid questions over the global demand outlook and rising supplies, particularly out of the United States.
"Will deeper OPEC supply curbs provide the panacea for the current oil market malaise? Probably not," said Stephen Brennock of oil broker PVM. "The oil cartel, therefore, faces an uphill battle to support oil prices."
In the United States, crude oil inventories fell by 4.3 million barrels last week, data from the American Petroleum Institute showed on Tuesday, compared with analyst expectations of a gain of 482,000 barrels.
Gasoline stocks were up by 3.3 million barrels, compared with a forecast gain of 1.3 million barrels in a Reuters poll.
Distillate fuel inventories, which include diesel and heating oil, fell by 141,000 barrels, against expectations of a 1 million barrel drop.
Official figures on oil and products are due from the Energy Information Administration later on Wednesday.