Oil prices steadied on Tuesday, remaining near two-month highs hit in the previous session, driven by expectations of stronger fuel demand during the summer travel season and the possibility of a U.S. interest rate cut.

Brent crude futures were up 20 cents at $86.80 a barrel by 0142 GMT, after rising 1.9 percent in the previous session to their highest close since April 30.

U.S. West Texas Intermediate crude rose 13 cents to $83.51 a barrel, after rising 2.3 percent to its highest since April 26.

Gasoline demand in the United States, the world's largest oil consumer, is expected to rise as the summer travel season begins with the Independence Day holiday this week.

On the supply side, markets are anticipating potential disruptions to U.S. refining and offshore production from Hurricane Beryl. The storm is currently forecast to move into Mexico’s Bay of Campeche and cause problems for oil production there.

Beryl hit the Caribbean as a Category 4 storm on Monday with the US National Hurricane Center warning of an extremely dangerous situation after it jumped from a Category 1 storm within 10 hours.