(Reuters) - Oil prices edged lower in early Asian trading hours on Tuesday as traders booked profits after prices rallied to their highest in over a month on Monday amid fears that the Middle East could be on the brink of a region-wide war.

Fighting in the Middle East intensified after Iran-backed Hezbollah fired rockets at Israel's third-largest city, Haifa, and Israel looked poised to expand its offensive into Lebanon, a year after the Hamas attack on Israel that sparked the Israel's ongoing war in Gaza.

Brent crude futures fell 23 cents, or 0.3%, to $80.70 per barrel by 0029 GMT. U.S. West Texas Intermediate futures fell 20 cents, or 0.3%, to $76.94 a barrel.

Both contracts rose over 3% on Monday to hit their highest levels since late-August, adding to last week's rally that saw them rise by over 8% for the biggest weekly gains in over a year.

The rally began after Iran launched a missile barrage on Israel on Oct. 1. Israel has sworn to retaliate and is weighing its options, with Iran's oil facilities considered a possible target.

However, some analysts believe that an attack on Iranian oil infrastructure is unlikely and have warned that oil prices could face considerable downward pressure if Israel focuses on any other target.

Even if an attack targets Iranian oil facilities, there is 7 million barrels per day of spare supply capacity within the Organization of Petroleum Exporting Countries (OPEC) to make up for the loss of its oil output, ANZ Bank analysts noted on Friday.

Meanwhile, Hurricane Milton intensified into a Category 5 storm on its way to Florida after forcing at least one oil and gas platform in the U.S. Gulf of Mexico to shut on Monday.

U.S. crude oil inventories are expected to rise by 1.9 million barrels in the week ended Oct. 4, according to a preliminary Reuters poll. The American Petroleum Institute is due to post its tally of U.S. stockpiles at 2030 GMT on Tuesday, followed by the official tally from the Energy Information Administration at 1430 GMT on Wednesday.

(Reporting by Shariq Khan in New York; Editing by Lincoln Feast.)