Brent crude futures rose 10 cents, or 0.2pc, to $55.03 a barrel by 0732 GMT, but were heading for a fifth weekly loss amid lingering fears over the impact of the virus.
US West Texas Intermediate (WTI) crude futures were up 6 cents, or 0.1pc, at $51.01 a barrel, also heading for a fifth consecutive week of losses.
Prices came off earlier highs in the session after China's central bank governor said the world's second-biggest economy may experience disruptions in the first quarter, while Japan announced a big jump in confirmed coronavirus cases among thousands of passengers confined to a cruise liner off its coast.
A panel advising the Organization of Petroleum Exporting Countries (OPEC) and allies led by Russia, known as the OPEC+ group, suggested provisionally cutting output by 600,000 barrels per day (bpd), three sources told Reuters on Thursday.
"We support this idea," said Sergei Lavrov, Russia's Foreign Minister, when asked about the proposal at a news conference in Mexico City later in the day.
The OPEC+ group, which pumps more than 40pc of the world's oil, has been withholding supply and agreed to deepen the cuts by 500,000 bpd from the start of this year, to 1.7 million bpd, nearly 2pc of global demand.
"The OPEC+ cuts are supportive of prices near term, but we are still facing uncertainty about the timing and speed of Chinese activity restarting post Chinese New Year," said Lachlan Shaw, head of commodities research at National Australia Bank in Melbourne.
Stimulus measures by the People's Bank of China (PBOC) are also supporting prices, Shaw said.
The PBOC has pumped hundreds of billions of dollars into the financial sector this week to help steady markets and boost the economy, along with other measures.
Eurasia group said it estimates a contraction in oil demand in China, the world's biggest importer of crude, of as much 3 million bpd in the first quarter from 2019, levels.
Meanwhile, JPMorgan cut its estimate for Brent to average $60.40 a barrel in 2020, down $4.1 compared with its earlier forecast.
Oil prices have fallen by more than a fifth since the outbreak of the virus in the city of Wuhan in China.
"There is still plenty of uncertainty around the global balance, with it unknown how demand will evolve in coming months as a result of the coronavirus," ING Economics said in a note.