Opec+ members voted to stick with the current plan of bringing 2 million barrels per day of production to the market, despite the prospect of a return of Iranian barrels if sanctions lift.
"The jury is still out" on the possible resumption of oil exports from Iran, Prince Abdulaziz bin Salman, Saudi Arabia's energy minister told reporters after a ministerial gathering of the group.
He added that the group did not discuss the possibility of Iranian supply recommencing either at its joint technical meeting on Monday nor at ministerial meetings on Tuesday.
Tehran, which resumed negotiations with the US to reinstate its nuclear deal, is looking to conclude talks before its presidential election begin on June 18.
Opec+, which is headed by Saudi Arabia and Russia, will "gradually return 2 million barrels a day (mb/d) of the adjustments to the market, with the pace being determined according to market conditions", the group said in a communique on Tuesday.
The group said conformity to its current levels of production cuts reached 114 per cent in April.
Following the meeting, Brent, the international benchmark, surged 2.76 per cent to reach $71.23 per barrel at 6.32pm UAE time. The benchmark rallied to levels last seen in May 2019 on expectations of tighter demand.
Brent moved above the $70 per barrel mark for the first time in two years during early trading on Tuesday.
West Texas Intermediate, which tracks US crude grades, was also trading at three-year highs, rising 3.57 per cent to $68.69 per barrel.
The North American benchmark reached the highest level seen since October 2018.
"Oil prices today are rising as the market is getting increasingly confident that demand is reaching the end of the recovery tunnel, with strong usage indications coming globally, from the US to China," said Louise Dickson, oil markets analyst at Rystad Energy.
"Any doubts about the current plan and plans for future supply policy will likely be addressed at the next meeting on 24 June to get a better pulse on the Iran nuclear negotiations and upstream implications, to make a better-educated call," she added.
Opec+ vowed to continue monthly monitoring meetings to observe oil market fundamentals. The group's next ministerial meeting will take place on July 1.
"The outcome is one we expected and built into our base case," Ann-Louise Hittle Wood Mackenzie's macro oils vice president, said. "Sticking to increases planned at the April meeting is what the market needs. Demand growth is outpacing supply gains even with the agreed month-by-month Opec+ production increases taken into account."