Brent was up by 81 cents at $58.56 a barrel by 1309 GMT.
The global benchmark has risen nearly 10pc since falling last week to its lowest this year.
U.S. oil was up 70 cents at $52.75 a barrel.
China, the world's second-largest economy, has imposed city lockdowns and travel restrictions to contain a virus that has now killed more than 2,000 people, stoking concern over an economic slowdown and a hit to oil demand.
"Those in doubt of the economic impact from the virus should take heed from Apple's surprise sales warning ... Put simply, this is the surest sign yet of the coronavirus fallout on the global economy," said PVM analysts in a note.
S&P Global Ratings said it expected coronavirus would deliver a "short-term blow" to economic growth in China in the first quarter, echoing findings by the International Energy Agency.
Official data showed new cases in China fell for a second straight day, although the World Health Organization said there was not enough data to know if the epidemic was being contained.
The oil market price structure is also showing signs that prompt demand for oil is picking up, as the front-month Brent futures market is moving deeper into backwardation, when near-term prices are higher than later-dated prices.
This week, oil prices were also buoyed by a U.S. decision to blacklist a trading subsidiary of Russia's Rosneft, which President Donald Trump's administration said provided a financial lifeline to Venezuela's government.
Hopes that the Organization of the Petroleum Exporting Countries and allied producers would deepen supply cuts also supported prices.
The grouping, known as OPEC+, has been withholding supply to support prices and meets next month to decide a response to the downturn in demand resulting from the coronavirus epidemic.
But in the United States, which is not party to any supply cut agreements, oil production has been rising.
U.S. shale production is expected to rise to a record 9.2 million barrels a day next month, the Energy Information Administration said.