SINGAPORE (Reuters) -Oil prices fell more than $1 on Tuesday as traders took profits from a rally in the previous session that lifted the market to its highest level in over a month amid fears that the Middle East could be on the brink of a region-wide war.

Brent crude futures fell $1.17, or 1.5%, to $79.76 per barrel at around 0420 GMT. U.S. West Texas Intermediate futures fell $1.19, or 1.6%, to $75.95 a barrel.

Both contracts rose over 3% on Monday to their highest levels since late-August, adding to last week's rally of 8%, the biggest weekly gain in over a year, on worries that escalating hostilities could disrupt oil supply from the Middle East.

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 Israel's ongoing war in Gaza.

"The geopolitical tensions in the Middle East rock on, but there has been some paring of exposure lately on some expectations that any disruptions to energy supplies may be more measured," said Yeap Jun Rong, market strategist at IG.

"Of course, more clarity still awaits on how Israel will retaliate towards Iran, and we may expect prices to remain supported amid the pricing of geopolitical risks."

The oil price 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 say an attack on Iranian oil infrastructure is unlikely, warning 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 to make up for the loss of its oil output, ANZ Bank analysts noted on Friday.

Developments in the Middle East will also do little to change the oil demand outlook, which continues to look somber, said Phillip Nova analyst Priyanka Sachdeva, adding the market was awaiting U.S. inflation data on Thursday for a view on the world's biggest economy.

While investors have been concerned about slow growth dampening fuel demand in China, the country's National Development and Reform Commission (NDRC) on Tuesday said it is fully confident of achieving its full-year economic targets.

In the U.S., 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.

Traders will be also looking out for the latest U.S. crude oil inventory data, with analysts expecting stocks 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.