Brent crude futures settled up $2.36, or 3.2%, at $75.44 a barrel, after Monday's rise of 4.6%. U.S. West Texas Intermediate crude rose $2.56, or 3.7%, to $72.05, building on a 4.9% gain the previous session. At the session highs on Tuesday, each contract was up more than $3.

Oil prices tumbled last week on concerns that vaccines might be less effective against the new Omicron variant, sparking fears that governments could impose fresh restrictions that would sink fuel demand.

However, a South African health official reported over the weekend that Omicron cases there had shown only mild symptoms while the top U.S. infectious disease official, Anthony Fauci, also said there did not appear to be "a great degree of severity" with the variant so far.

"The market was oversold as a knee-jerk reaction to Omicron and its potential spread and impact on travel restrictions," said Gary Cunningham, director of market research at Tradition Energy. "Now we're seeing the market go back to expectations of strong demand over the next 6-12 months."

In another sign of confidence in oil demand, the world's top exporter, Saudi Arabia, raised monthly crude prices on Sunday.

Last week, the Organization of the Petroleum Exporting Countries and its allies, a group known as OPEC+, agreed to keep raising output by 400,000 barrels per day (bpd) in January despite release of U.S. strategic petroleum reserves.

"The market is starting to take this variant in its stride," said Matt Smith, an analyst at data and analytics firm Kpler.

Analysts polled by Reuters forecast that U.S. crude inventory data would show a second straight weekly decline. Weekly industry data is due at 4:30 p.m. ET, followed by government figures on Wednesday. [EIA/S]

Oil prices were also supported by delays to the return of Iranian oil, with indirect nuclear talks between the United States and Iran having hit stumbling blocks. Germany urged Iran on Monday to present realistic proposals in talks over its nuclear programme.

(Additional reporting by Noah Browning and Florence Tan; Editing by Marguerita Choy, David Goodman and David Gregorio)

By Nia Williams