Brent crude futures rose 81 cents, or 0.9%, to $88.70 a barrel by 0344 GMT, reversing a 0.6% loss on Friday.
U.S. West Texas Intermediate (WTI) crude futures gained 72 cents, or 0.9%, to $85.86 a barrel, having fallen 0.5% on Friday.
Both benchmarks rose for a fifth week in a row last week, gaining around 2% to hit their highest since October 2014. Prices are already up more than 10% this year on the concerns over tightening supplies.
"An expectation for higher heating oil demand in the United States amid cold weather also added to pressure," he said.
In the Middle East, the United Arab Emirates' defence ministry said it destroyed two Houthi ballistic missiles targeting the Gulf country on Monday, with no casualties, the state news agency (WAM) reported.
The OPEC+, which groups the Organization of the Petroleum Exporting Countries (OPEC) with Russia and other producers, is struggling to hit its monthly output increase target of 400,000 barrels per day (bpd).
OPEC+ compliance with long-installed oil production cuts rose to about 122% in December, two sources from the producer group told Reuters, indicating that some members continue to struggle to raise their output.
"Expectations that OPEC+ members such as Saudi Arabia and Russia are likely to keep the current policy of gradual increase of output to maintain Brent oil prices between $85 and $90 a barrel are providing support to an overall sentiment," said Tetsu Emori, CEO of Emori Fund Management Inc.
Money managers raised their net long U.S. crude futures and options positions in the week to Jan. 18, the U.S. Commodity Futures Trading Commission (CFTC) said on Friday.
In the United States, petroleum inventories have continued to slide over the last month, while energy firms cut oil rigs this week for the first time in 13 weeks. Analysts expect cold weather to boost heating demand over the next few weeks.
