Brent crude gained 16 cents, or 0.2%, at $81.91 a barrel at 0406 GMT, while U.S. West Texas Intermediate (WTI) crude was up 15 cents, or 0.2%, at $79.05 a barrel.
Oil prices gained 5% last week after protests in Kazakhstan disrupted train lines and hit production at the country's top oilfield Tengiz, while a pipeline maintenance in Libya pushed production down to 729,000 barrels per day from a high of 1.3 million bpd last year.
Kazakhstan's largest oil venture Tengizchevroil (TCO) is gradually increasing production to reach normal rates at the Tengiz field after protests limited output there in recent days, operator Chevron said on Sunday.
"Growing supply outages in places like Libya and others have re-centered the spotlight on supply availability," RBC Capital analysts said in a note.
Oil is also drawing support from rising global demand and lower-than-expected supply additions from the Organization of the Petroleum Exporting Countries, Russia and allies, or OPEC+.
OPEC's output in December rose by 70,000 bpd from the previous month, versus the 253,000 bpd increase allowed under the OPEC+ supply deal which restored output slashed in 2020 when demand collapsed under COVID-19 lockdowns.
U.S. energy firms kicked off the new year by continuing to add oil and natural gas rigs after increasing the rig count in 2021 after two years of declines.
The oil and gas rig count, an early indicator of future output, rose two to 588 in the week to Jan. 7, its highest since April 2020, energy services firm Baker Hughes Co said in its closely followed report on Friday.
Globally, governments from Europe to China and India have put in some curbs as they grapple with the highly transmissible Omicron variant.
In the United States, employment increased less than expected in December amid worker shortages, and job gains could remain moderate in the near term as spiralling COVID-19 infections disrupt economic activity.
