U.S. West Texas Intermediate (WTI) crude oil futures were trading up 8 cents at $52.45 per barrel at 0231 GMT.
Brent crude futures, the international benchmark for oil prices, were down 14 cents at $55.72 a barrel, Reuters reported.
Traders said markets were receiving some support from top crude exporter Saudi Arabia, which said it would adhere strictly to its commitment to cut output under the global agreement among oil producers including the Organization of the Petroleum Exporting Countries (OPEC) and Russia.
"Many countries are actually going the extra mile and cutting beyond what they've committed ... I am confident about the impact ... and I am very encouraged about those first two weeks," Saudi Energy Minister Khalid al-Falih said late on Monday at an industry event in Abu Dhabi.
Under the agreement, OPEC, Russia, and other non-OPEC producers have pledged to cut oil output by nearly 1.8 million barrels per day (bpd), initially for six months, to bring supplies back in line with consumption.
Despite this, crude prices have fallen almost 5 percent since their early January peaks, as financial oil traders remain skeptical about OPEC's and Russia's willingness to fully comply with the cuts.
Recent fires which have caused unplanned closures at refineries in the Middle East and Asia have also hit short-term demand for crude in the region, traders said.
Analysts also said that steps to prop up oil prices through a cut in supplies could be self-defeating.
AB Bernstein said on Tuesday that the production cuts, and resulting higher prices, would likely hit oil demand.
"For each $10 per barrel increase in oil prices, oil demand will decline by 10 basis points. While consensus expects demand-growth of 1.3 million bpd in 2017 (vs 1.4 million bpd in 2016), we see risks to the downside as demand growth in China and India starts to moderate," Bernstein said.