Crude last week jumped more than 6% after OPEC+, the Organization of the Petroleum Exporting Countries (OPEC) and allies including Russia, surprised the market with a new round of production cuts starting in May.

Brent crude rose 19 cents, or 0.2%, to $85.31 a barrel by 1200 GMT on Monday, while U.S. West Texas Intermediate crude gained 9 cents to $80.79, Reuters reported.

"Those who were bearish are questioning the demand outlook in light of the cuts, whilst clearly those who were bullish are now seeing even a tighter market over the second half," ING's head of commodities research Warren Patterson said.

"I am in the latter camp and still see prices moving higher from here as we go through the year."

Adding to tightness in supply has been a shutdown of Iraq's northern exports. A deal was signed last week to restart the flows, but as of Thursday they hadn't resumed.

Oil also drew support from a steeper-than-expected drop in U.S. crude inventories last week, as well as a decline in gasoline and distillate stocks, hinting at rising demand.

In global financial markets, a U.S. inflation report to be released on Wednesday could help investors gauge the near-term trajectory for interest rates.

"This week's U.S. data could be a drag on sentiment if strong numbers reinforce expectations of the Fed continuing on its tightening path, while weak numbers point to economic pain, which means either way, risk-aversion grows," said Vandana Hari, founder of oil market analysis provider Vanda Insights.

Also coming up are monthly reports from OPEC on Thursday and the International Energy Agency on Friday, which will update oil demand and supply forecasts.