Brent crude futures were up 49 cents, or 0.7%, at $71.84 a barrel by 0233 GMT, the highest since September 2019. The international benchmark gained 1.6% on Wednesday.
U.S. West Texas Intermediate crude futures rose 44 cents, or 0.6%, to $69.27 a barrel. Prices earlier rose to as much as $69.32, the most since October 2018, after gaining 1.5% in the previous session.
The consensus among market forecasters, including the Organization of the Petroleum Exporting Countries and its allies, known as OPEC+, is that oil demand will exceed supply in the second half of 2021, which has spurred the recent run in prices.
OPEC+ data shows that by the end of the year oil demand will be 99.8 million barrels per day (bpd) versus supply of 97.5 million bpd.
This rebalancing will be led by resurgent demand in the United States, the world's biggest oil user, from vehicle consumption this summer, along with rising fuel needs in China, the world's second biggest oil consumer, and in the UK as it exits its COVID-19 lockdowns.
"The U.S. driving season is a period that sees higher‑than‑normal fuel consumption. UK traffic is now sitting above pre‑pandemic levels," CBA commodities analyst Vivek Dhar said in a note. "We continue to see the oil demand recovery led by the U.S., Europe and China."
OPEC+ agreed on Tuesday continue with plans to ease supply curbs through July. read more
The OPEC+ meeting last 20 minutes, the quickest in the grouping's history, suggesting strong compliance among members and the conviction that demand will recover once the COVID-19 pandemic shows sign of abating.
A slowdown in talks between the U.S. and Iran over the latter's nuclear programme has also reduced expectations for Iranian oil supply to come back to the market this year.
The European Union envoy coordinating the discussions said he believed a deal would be struck at the next round of talks starting next week, though other diplomats cautioned that difficulties remain.
"The current talks in Vienna to revive the 2015 nuclear accord, which would see U.S. sanctions on Iran lifted, now look unlikely to find a resolution," said CBA's Dhar.