Brent crude futures rose 42 cents, or 0.6%, to $64.09 a barrel at 0421 GMT, after gaining 39 cents on Tuesday.
U.S. West Texas Intermediate (WTI) crude futures added 40 cents, or 0.7%, to $60.58 a barrel, following Tuesday's rise of 48 cents.
Signs of a strong economic recovery in China and the United States have underpinned recent oil price gains, but concerns over stalled vaccine rollouts worldwide and soaring COVID-19 infections in India and Brazil have capped gains.
A lower greenback, which hit three-week lows on Wednesday, makes crude purchases cheaper for countries using other currencies.
The Organization of the Petroleum Exporting Countries (OPEC) tweaked up its forecast on Tuesday for world oil demand growth this year, now expecting demand to rise by 5.95 million barrels per day (bpd) in 2021, up by 70,000 bpd from its forecast last month. It is banking on the pandemic to subside and travel curbs to be eased.
Further supporting the market on Wednesday, sources said data from the American Petroleum Institute showed crude stocks fell by 3.6 million barrels in the week ended April 9, compared with estimates for a decline of about 2.9 million barrels from analysts polled by Reuters. [API/S]
Traders are waiting to see if official inventory data from the U.S. Energy Information Administration (EIA) on Wednesday matches that view.
Market gains are being capped on concerns about increased oil production in the United States and rising supply from Iran at a time when OPEC and its allies are set to bring on more supply from May.
EIA said this week oil output from seven major shale formations is expected to rise by 13,000 bpd in May to 7.61 million bpd.