Brent crude was at $54.94 a barrel by 0824 GMT, up 49 cents, or nearly 0.9pc, and U.S. West Texas Intermediate (WTI) crude was up 68 cents, or 1.3pc, at $50.79.
Despite Tuesday's gains, an extended slide over the last two weeks on concern over the global economic impact of the coronavirus means prices are still more than 20pc lower than this year's peak on Jan. 8. Monday's drop left crude prices at their lowest in more than a year.
People familiar with the matter told Reuters on Monday that the Organization of the Petroleum Exporting Countries (OPEC) and its allies including Russia, known as OPEC+, were considering cutting crude output by a further 500,000 barrels per day (bpd) due to the impact on demand from the coronavirus.
"A some half-a-million barrels (per day) cut is expected but we won't rule out an even deeper cut should the situation worsen," said Margaret Yang, analyst at CMC Markets. "This expectation boosted oil trading today."
Despite the return to calmer trading, mirroring other financial markets on Tuesday, Goldman Sachs warned that while it sees oil producers responding to the situation by cutting supply, the coronavirus outbreak's impact on demand is likely to keep volatility in spot prices elevated.
The coronavirus has now claimed more than 420 lives in China and resulted in deaths in the Philippines and Hong Kong.
"Oil prices are now at levels where we would expect a supply response from both OPEC and shale producers, and where China would likely seek to build crude inventories," Goldman said in a note.
Still, other warned that any failure by OPEC+ to take what investors deem suitably robust action to limit the impact of the virus on oil markets could trigger further price drops.
"If OPEC+ fails to deliver an emergency response to the coronavirus, crude prices could slump another 10pc," said Edward Moya, market analyst at OANDA, in an email to Reuters.
Even if supply cuts are imposed, Moya said, their impact could be outstripped by the virus.
"Expectations are growing that Saudi Arabia will do whatever it takes to make sure the oil producing alliance delivers deeper cuts," he said.
"But it might not matter if the virus shows no sign of easing."
UBS has revised its oil demand growth estimate for 2020, down to 0.9 million bpd from 1 million bpd, and it expects OPEC+ to extend its supply cuts to the year-end.