May 24 (Reuters) - Oil prices were steady early in the session on Friday as players took stock of the U.S. Federal Reserve's latest comments on interest rates amid sticky inflation, while firming seasonal U.S. fuel demand lent support.

Brent crude futures were up 1 cent at $81.37 a barrel at 0002 GMT. U.S. West Texas Intermediate crude (WTI) futures were down 2 cents at $76.85.

Both benchmarks settled at multi-month lows on Thursday, with Brent crude futures closing at their weakest point since January and U.S. crude futures hitting a three-month low.

Ongoing macroeconomic constraints in the U.S. held prices in the balance as investors digested Wednesday's minutes from the Fed's latest policy meeting, which showed policymakers remain doubtful if current interest rates are high enough to tame stubborn inflation.

Some officials said they would be willing to hike borrowing costs again if inflation surged. However, Fed Chair Jerome Powell and other policymakers have since said they feel further rate hikes are unlikely.

Meanwhile, strengthening U.S. gasoline demand was helping to stabilise prices ahead of the Memorial Day holiday weekend, which is considered the start of the U.S. summer driving season.

Gasoline demand in the U.S. reached its highest level since November, the Energy Information Administration (EIA) said on Wednesday. That helped support the market as U.S. drivers account for around a tenth of global oil demand, "making the upcoming driving season a pillar of the recovery in global demand growth", ANZ analysts said in a note.

All eyes are now on the Organization of the Petroleum Exporting Countries and allies, together called OPEC+, set to meet on June 1, where they are expected to discuss whether to extend voluntary oil output cuts of 2.2 million barrels per day.

"The market is also tentative about taking an aggressive positioning ahead of next week’s OPEC meeting, where supply policy will be discussed," ANZ analysts added. (Reporting by Georgina McCartney in Houston; Editing by Sonali Paul)