Brent crude futures recorded gains of 24 cents, or 0.28%, to $86.42 per barrel by 0405 GMT after settling 0.4% higher on Monday.
U.S. West Texas Intermediate crude was at $80.69 per barrel, up 23 cents, or 0.29%, following a 1% gain in the previous session.
Brent prices are on track to rise for the sixth straight session, the longest stretch of gains since May 2022, buoyed by hopes of China's demand recovery and as new refining capacity in Asia and Middle East is being ramped up, processing more crude.
"The supply concerns that helped oil prices higher overnight likely stemmed from Chevron's CEO comment that there's 'not a lot of swing capacity' in oil markets," Commonwealth Bank of Australia analyst Vivek Dhar said in a note.
"The key unknown for 2023 will be the disruption to Russia's oil and refined product exports."
Chevron Corp chief executive Mike Wirth said ships carrying Russian crude and products now have to travel over longer distances to reach non-sanctioned markets while oil inventories and swing supplies are limited, making the global market vulnerable to any unexpected supply disruption.
Traders are keenly awaiting China's oil trade data for January and February later on Tuesday, looking for signals of a recovery in demand following Beijing's lifting of pandemic controls late last year.
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