Brent crude was at $57.29 a barrel, down 5 cents by 0946 GMT after rising 5.2pc last week, the biggest weekly gain since September 2019.
U.S. West Texas Intermediate crude rose 5 cents to $52.10 a barrel, after a 3.4pc gain last week.
Japan, the world's fourth-largest oil consumer, reported an economic contraction of 6.3pc for the October to December period and there is an expectation of a further contraction in the January to March quarter because of the contagion.
Singapore, whose trade-dependent economy is a barometer for the region, also warned of the potential for a recession this quarter because of the outbreak.
"Oil remains acutely vulnerable to both excess supply and the economic coronavirus-induced slowdown in China and other parts of Asia," Jeffrey Halley, a senior market analyst at OANDA in Singapore said.
The International Energy Agency (IEA) said last week the virus is set to cause oil demand to fall by 435,000 barrels per day (bpd) in the first quarter of 2020, from the same period a year ago, in what would be the first quarterly drop since the financial crisis in 2009.
Oil did rise last week for the first time since early January on optimism that Chinese economic stimulus measures amid the outbreak could lead to a recovery in oil demand in the world's largest importing country.
There are some indications of prompt demand for oil as the front-month Brent futures market has shifted to a backwardation, when near-term prices are higher than later-dated prices, from a contango.
Investors are also anticipating that the Organization of the Petroleum Exporting Countries and its allies, including Russia, will approve a proposal to deepen production cuts to tighten global supplies and support prices.
The group, known as OPEC+, has an agreement to cut oil output by 1.7 million bpd until the end of March.
A technical committee earlier this month recommended the group reduce production by another 600,000 bpd because of the impact from the coronavirus, though oil prices' first weekly gain since early January on Friday may give the producers pause.
"The more recent strength that we have seen in the market may also make OPEC+ complacent when it comes to taking action," ING said in a note.
"Already the group has failed to bring forward the meeting that was originally scheduled for early March. And if the market consolidates around current levels, OPEC+ may see little need to rush a decision."