Brent crude futures climbed USD 1.64, or 2.08%, to USD 80.66 a barrel by 1041 GMT, while U.S. crude futures were at USD 76.38 a barrel, up USD 1.55, or 2.07%.
Prices jumped after Libya's eastern-based Benghazi government announced the closure of all oil fields on Monday, halting production and exports.
"The biggest risk for oil market is probably a further drop in Libyan oil production due to political tensions in the country," said analyst Giovanni Staunovo of Swiss bank UBS.
Oil prices opened the week higher after Hezbollah fired hundreds of rockets and drones into Israel on Sunday and Israel's military said it struck Lebanon with around 100 jets to thwart a larger attack, in one of the biggest clashes in more than 10 months of border warfare.
The clash raised fears of wider conflict in the region.
"Geopolitical risk factors will likely influence the oil market significantly," said Kelvin Wong, a senior market analyst at OANDA in Singapore.
Monday's gains follow from both oil benchmarks gaining over 2% on Friday after U.S. Federal Reserve Chair Jerome Powell endorsed the start of interest rate cuts.
"The prospect of easing monetary policy boosted sentiment across the commodity complex," ANZ analysts said in a note.
Investors remain cautious over the actions of the Organization of Petroleum Exporting Countries (OPEC) and its allies, or OPEC+, which has plans to raise output later this year, said Priyanka Sachdeva, senior market analyst at Phillip Nova.
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