Brent crude was up 91 cents, or 0.8%, at $120.63 a barrel at 0343 GMT after touching an intraday high of $121.95, extending a 1.8% gain from Friday.
U.S. West Texas Intermediate (WTI) crude futures were up 93 cents, or 0.8%, at $119.80 a barrel after earlier hitting a three-month high of $120.99. It gained 1.7% on Friday.
Saudi Arabia raised the official selling price (OSP) for its flagship Arab light crude to Asia to a $6.50 premium versus the average of the Oman and Dubai benchmarks, from a $4.40 premium in June, state oil producer Aramco said on Sunday.
The July OSP is the highest since May, when prices hit all-time highs due to worries of disruption in supplies from Russia.
The price hike came despite a decision last week by the Organization of the Petroleum Exporting Countries and allies, together called OPEC+, to increase output in July and August by 648,000 barrels per day, or 50% more than previously planned.
Iraq said on Friday it plans to raise output to 4.58 million bpd in July.
Oil producers are "making hay while the sun shines", Avtar Sandu, manager of commodities at Phillip Futures in Singapore said, adding that U.S. summer driving demand and easing of COVID-19 lockdowns in China are expected to keep prices high.
The OPEC+ move to bring forward output hikes is widely seen as unlikely to meet demand as the increased allocation is spread across all members, including Russia that is facing sanctions.
"While that increase is sorely needed, it falls short of demand growth expectations, especially with the EU's partial ban on Russian oil imports also factored in," Commonwealth Bank analyst Vivek Dhar said in a note.
Separately, Italy's Eni and Spain's Repsol could begin shipping Venezuelan oil to Europe as soon as next month to make up for Russian crude, five people familiar with the matter told Reuters, resuming oil-for-debt swaps halted two years ago when Washington stepped up sanctions on Venezuela.
However, the volume that the companies will receive is not expected to be large, the people said.
