Brent crude futures were up 31 cents, or 0.5pc, at $62.35 a barrel by 0741 GMT after falling 1.9pc the previous session. For the week, Brent is down about 4pc.
U.S. West Texas Intermediate futures were up 27 cents, or 0.5pc higher at $55.86 a barrel.
The contract fell 2pc on Thursday and is 4.6pc lower for the week.
"Oil's sell-off (for the week) continued at pace as fears continued about the effects on global demand from a virus-induced economic slowdown in Asia," said Jeffrey Halley, senior market analyst, OANDA. "We would expect the fragility in oil prices to continue."
Offering support for prices was news that U.S. crude oil and distillate inventories fell last week, the Energy Information Administration said on Thursday.
Though they failed to match analysts' expectations in a Reuters poll of a 1 million barrel drop, crude inventories did decline by 405,000 barrels in the week to Jan. 17, government data showed.
"(The) sell-off on the ... flu scare was mollified by a timely decline in U.S. crude inventories," said Stephen Innes, market strategist at AxiTrader.
The virus has infected more than 800 so far in China, with 25 dead as of Thursday, according to China's National Health Commission. The World Health Organisation has declared the situation an emergency, but stopped short of declaring the epidemic of international concern.
Most of the cases are in the central Chinese city of Wuhan, where the virus is believed to have originated late last year, though cases have now been found in at least seven other countries.
"Oil prices could remain on a slippery slope as traders remain incredibly twitchy about the effects the coronavirus outbreak could have on Chinese GDP and air travel more broadly," said AxiTrader's Innes.