US crude futures were at $36.67 per barrel at 0632 GMT, up 17 cents from their last settlement and 40 percent above February's 2016 low.
Brent crude futures were at $39.84 per barrel, up 19 cents and over 40 percent higher than 2016 lows hit in January.
Analysts said falling US output was lending support to the market but that concerns over slowing demand and an ongoing global production and storage overhang was capping any potential for bigger price gains.
Energy consultancy Wood Mackenzie said in a report to clients that it expected "the annual average price for 2016 being lower than 2015 and then recovering in 2017, reflecting large oversupply and high stock levels during the first half of 2016."
Singapore-based brokerage Phillip Futures said that under current conditions the highs of $40 to $41 per barrel for Brent crude reached earlier this week were "as high as it can go".
Price gains were also capped by a strengthening US dollar, which reversed recent losses against leading currencies, potentially hampering demand as dollar-denominated crude gets more expensive as the greenback rises.
Also preventing a fundamental shift towards higher prices is a concern over faltering demand in China, where the economy is growing at its slowest pace in a generation. China's February trade performance was far worse than economists had expected, with exports tumbling the most in over six years.
Although China imported record crude volumes of 8 million barrels per day (bpd) in February, analysts expect this figure to fall as the Beijing scales back buys for its strategic reserves, and car sales begin to fall as the sharp economic slowdown starts to show results.
Additionally, chances of a coordinated freeze in production to halt a ballooning global supply glut of over 1 million bpd above consumption are ebbing as OPEC-member Kuwait said it would only cap output if all major producers participate, including Iran, which has balked at the plan.
One key factor in determining the oil market balance will be US output, which the government said would be 8.19 million bpd in 2017, down from over 9 million bpd currently.
Fresh US output data is scheduled to be published later on Wednesday.
Yet even if US production falls at the expected rate, many analysts including Goldman Sachs say they expect oil prices will only rise gradually, if at all, this year.
