U.S. West Texas Intermediate (WTI) crude futures rose 7 cents, or 0.10%, to $67.79 as of 0500 GMT, extending a 2.1% gain following the Memorial Day holiday in the United States on Monday. Prices rose to their highest since October 2018.
Brent crude futures climbed 17 cents, or 0.24%, to $70.42 a barrel, after rising 1.3% overnight, when it hit its highest since March 8.
The Organization of the Petroleum Exporting Countries (OPEC) and its allies, together called OPEC+, agreed on Tuesday to keep to their plan to gradually ease supply curbs through July.
Saudi Energy Minister Prince Abdulaziz bin Salman's comments after the meeting buoyed the market. He said he saw a solid demand recovery in the United States and China and added that the pace of vaccine rollouts "can only lead to further rebalancing of the global oil market".
"The market appears focused on the more constructive outlook for later this year, with OPEC+ of the view that the market will see significant stock drawdowns between September and the end of the year," ING Economics analysts said in a note.
Including extra cuts by Saudi Arabia tapering off through July, the producer group will be returning 700,000 barrels per day (bpd) in June and 840,000 bpd in July, ING said.
Market gains over the past two weeks have been capped by concerns about a potential lifting of oil sanctions against Iran, as talks on reviving a nuclear accord made progress. However, negotiations hit a roadblock this week.
Two Western diplomats and an Iranian official said the talks would likely pause on Thursday, but it was unclear if talks would resume before Iran's June 18 presidential election.
"The return of Iranian barrels does not appear to be an imminent issue for the oil market with the fifth round of nuclear negotiations in Vienna failing to produce a major diplomatic breakthrough," analysts at RBC Capital Markets said in a note.
That should provide breathing room for demand to catch up, some analysts said.
"The delay is pushing the threat of another 2 million bpd of oil (returning to the market) to later in the year, when further economic growth should buffer its impact," ANZ Research analysts said in a note.
OPEC Secretary General Mohammad Barkindo also played down any potential disruption to the market, saying the group expected any return of Iranian exports "will occur in an orderly and transparent fashion" if and when a nuclear deal is reached.
