Brent crude futures struck a high of $US82.37 ($A115.93) a barrel and was at $US79.34 ($A111.67), up $US6.47 ($A9.11), or 8.88 per cent, by 23:05 GMT on Sunday (10:05 AEDT Monday).
US West Texas Intermediate crude jumped $US5.36 ($A7.54), or eight per cent, to $US72.38 ($A101.87) a barrel after touching a high of $US75.33 ($A106.02) earlier.
Israel launched a new wave of strikes on Tehran on Sunday and Iran responded with more missile barrages, a day after the killing of Supreme Leader Ali Khamenei pitched the Middle East and the global economy into deepening uncertainty.
At least three tankers were damaged off the Gulf coast and one seafarer was killed as Iranian retaliation for US and Israeli strikes on Iran exposed ships to collateral damage, shipping sources and officials said on Sunday.
Meanwhile the Organization of Petroleum Exporting Countries, in a Sunday meeting said it would increase production by 206,000 barrels per day in April, which was more than analysts had been expecting.
The countries boosting output include Saudi Arabia, Russia, Iraq, the United Arab Emirates, Kuwait, Kazakhstan, Algeria and Oman.
Roughly 15 million barrels of crude oil per day - about 20 per cent of the world's oil - are shipped through the Strait of Hormuz, making it the world's most critical oil chokepoint, according to Rystad Energy.
Tankers travelling through the strait, which is bordered in the north by Iran, carry oil and gas from Saudi Arabia, Kuwait, Iraq, Qatar, Bahrain, the UAE and Iran.
Iran had temporarily shut down parts of the strait in mid-February for what it said was a military drill. Further disruptions to that shipping channel could lead to lower supply and higher prices for oil.
"Roughly one-fifth of global oil supply passes through the Strait of Hormuz, a vital artery for world trade, meaning markets are more concerned with whether barrels can move than with spare capacity on paper," said Jorge León, Rystad's senior vice president and head of geopolitical analysis.
"If flows through the Gulf are constrained, additional production will provide limited immediate relief, making access to export routes far more important than headline output targets."
Iran exports roughly 1.6 million barrels of oil a day, mostly to China, which may need to look elsewhere for supply if Iran's exports are disrupted, another factor that could increase energy prices.
