Brent crude rose 66 cents, or 1.1pc, to $60.17 a barrel by 0951 GMT.
U.S. crude was up 62 cents, or 1.2pc, at $54.10 a barrel.
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 the 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 wants to extend oil production cuts until at least June from March, and may 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.
"A further extension is a strong possibility and a deeper cut is a possibility," one OPEC source told Reuters. Any fallout of the China virus on oil demand is likely to be clearer over the coming week, the source said.
In the United States, crude oil inventories fell by 4.3 million barrels last week, data from industry group the American Petroleum Institute showed on Tuesday, compared with analysts' expectations of a gain of 482,000 barrels.
Gasoline stocks were up by 3.3 million barrels, compared with forecasts in a Reuters poll of a 1.3 million-barrel gain.
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 out from the Energy Information Administration later on Wednesday.