Brent crude futures nudged 6 cents higher to $86.37 a barrel by 0350 GMT, while U.S. West Texas Intermediate crude was at $82.56 a barrel, up 4 cents.
Both contracts notched their fourth weekly gains last week - the longest-such streak since mid-2022 - after the International Energy Agency (IEA) forecast record demand in 2023 of 101.9 million barrels per day (bpd), up 2 million bpd on last year.
However, the IEA warned in its monthly report that the output cuts announced by OPEC+ producers risked exacerbating an oil supply deficit expected in the second half of the year and could hurt consumers and a global economic recovery.
Rising costs for Middle East crude supplies, which meet more than half of Asia's demand, are already squeezing refiners' margins, prompting them to secure supplies from other regions.
Refiners are also ramping up gasoline output ahead of peak summer demand, while cutting diesel production amid worsening margins.
"While the flat price and time spreads have strengthened on the back of expectations of a tighter market, demand concerns clearly remain," ING analysts said in a note.
"Weaker refinery margins remain a feature, with the weakness predominantly driven by middle distillates. Stronger crude prices will not be helping margins for refiners either."
Meanwhile, oil exports from northern Iraq to the Turkish port of Ceyhan remained at a standstill almost three weeks after an arbitration case ruled Ankara owed Baghdad compensation for unauthorised exports.
Investors will be watching for the release of China's first quarter gross domestic product (GDP) data this week, which is expected to be positive for commodity prices, CMC Markets analyst Tina Teng said.
Earnings from U.S. companies could also provide clues for the Federal Reserve's policy path and the dollar's trajectory, she added.
The greenback has been strengthening alongside interest rate hikes, making dollar-denominated oil more expensive for holders of other currencies.
Traders are betting that the Fed will raise its lending rate in May by another quarter of a percentage point and pushed out to late this year expectations of a rate cut, as typically occurs in a slowdown.
The market is pricing in a 78% chance of a 25 basis points (bps) rate hike in May, with fewer than 60bps of cuts priced in by the end of the year, IG Analyst Tony Sycamore said.
"(That) means some of the supportive tailwinds for crude oil demand from expectations of Fed rate cuts are starting to fade," he added.
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