Brent crude futures for August climbed 26 cents, or 0.4%, to $75.16 a barrel by 0400 GMT, paring earlier losses. It rose as high as $75.23 a barrel, the strongest since April 25, 2019, earlier in the session.
U.S. West Texas Intermediate (WTI) crude for July was at $73.70 a barrel, up 4 cents, or 0.1%. WTI for August climbed 11 cents, or 0.2%, to $73.23 a barrel.
Brent gained 1.9% and WTI jumped 2.8% on Monday.
Both benchmarks have risen for the past four weeks on optimism over the pace of global COVID-19 vaccinations and expected pick-up in summer travel. The rebound has pushed up spot premiums for crude in Asia and Europe to multi-month highs.
"The market sentiment stays strong with improved outlook for global demand," said Satoru Yoshida, a commodity analyst with Rakuten Securities, adding that a rally in Asian stock markets is also helping boost risk appetite among investors.
Global shares extended their recovery on Tuesday, with Asian markets bouncing from four-weeks lows as investor focus on economic growth partly offset worries about the U.S. Federal Reserve raising rates sooner than expected.
BofA Global Research raised its Brent crude price forecasts for this year and next, saying that tighter oil supply and recovering demand could push oil briefly to $100 per barrel in 2022.
Investors are looking to weekly U.S. inventory data as crude oil stockpiles have fallen for four weeks, said Toshitaka Tazawa, analyst at commodities broker Fujitomi Co.
U.S. crude stocks were expected to drop for the fifth consecutive week, while distillate and gasoline were seen rising last week, a preliminary Reuters poll showed on Monday.
"The oil prices are expected to hold a firm tone amid expectations that fuel demand will pick up quickly along with economic recovery in Europe and the United States," Tazawa said.
The price gap between the world's two most actively traded oil contracts narrowed to its lowest in more than seven months, demonstrating that U.S. oil output is still in the COVID-19 doldrums with the market likely to remain undersupplied.
Negotiations to revive the Iran nuclear deal took a pause on Sunday after hardline judge Ebrahim Raisi won the country's presidential election.
Raisi on Monday backed talks between Iran and six world powers to revive a 2015 nuclear deal but flatly rejected meeting U.S. President Joe Biden, even if Washington removed all sanctions.
"The lower probability of Iranian crude oil returning to the market due to the new hardline president is also supporting the market," Fujitomi's Tazawa said.
