Goldman Sachs has also raised its 2020 oil price forecasts, with Brent now seen at $40.40 a barrel and WTI at $36 a barrel
Oil prices climbed on Tuesday as the easing of coronavirus lockdown measures across the globe lifted trader hopes for a swift recovery in demand, though gains were capped by the spectre of persistent oversupply in the market.
Brent crude futures rose 0.3%, or 14 cents, by 0435 GMT to $40.94 a barrel. The benchmark contract had fallen $1.50 on Monday, snapping a seven-day streak of gains.
US West Texas Intermediate (WTI) crude futures rose 0.7%, or 26 cents, to $38.45 a barrel, after dropping by $1.36 on Monday.
"With Brent holding very nicely above $40, there's talk among traders that WTI will test that level soon," said Michael McCarthy, chief market strategist at CMC Markets.
Goldman Sachs has also raised its 2020 oil price forecasts, with Brent now seen at $40.40 a barrel and WTI at $36 a barrel.
Tuesday's gains came as New York, the US city hardest hit by the novel coronavirus outbreak, began reopening on Monday after about three months, potentially spurring fuel demand.
US crude and gasoline inventories are estimated to have fallen by 1.5 million barrels and about 100,000 barrels respectively in the week to June 5, a preliminary Reuters poll showed ahead of a report from the American Petroleum Institute industry group later on Tuesday.
However distillate inventories, which include diesel and heating oil, were seen rising by 2.9 million barrels.
"You've got demand recovering gradually but steadily," said Lachlan Shaw, head of commodity research at National Australia Bank. "However there's still massive excess supply, so OPEC and friends need to control barrels coming into the market."
The Organization of the Petroleum Exporting Countries (OPEC), Russia and other producers, a grouping known as OPEC+, on Saturday agreed a one-month extension through July of a record 9.7 million barrels per day output cut.