Energy markets are particularly nervous because the crisis is unfolding around the Strait of Hormuz, through which roughly one-fifth of the world's oil supply normally passes.
Disruptions in tanker movements and rising security risks have already slowed shipping activity, leaving Asian buyers especially vulnerable given their heavy reliance on Middle Eastern crude.
Brent crude futures were up $US24.96 ($A35.71) or 27 per cent at $US117.65 ($A168.33) per barrel at 0451 GMT on Monday - on track for the biggest-ever jump in a single day.
US West Texas Intermediate (WTI) crude futures were up $US25.72 ($A36.80), or 28.3 per cent, to $US116.62 ($A166.86).
WTI surged 31.4 per cent to a session high of $US119.48 ($A170.95) a barrel earlier on Monday, while Brent rose as much as 29 per cent to $US119.50 ($A170.98) a barrel.
Before the surge on Monday, Brent had already climbed 27 per cent and WTI by 35.6 per cent last week.
"Unless oil flows through the Strait of Hormuz resumes soon and regional tensions ease, upward pressure on prices is likely to persist," said Vasu Menon, managing director for investment strategy at OCBC in Singapore.
Iraq and Kuwait have begun cutting oil output, adding to earlier liquefied natural gas reductions from Qatar, as the war blocks shipments from the Middle East.
Analysts expect the UAE and Saudi Arabia will have to cut output soon as they run out of oil storage.
Also boosting prices is the appointment of Mojtaba Khamenei to succeed his father Ali Khamenei as Iran's supreme leader, signalling hardliners remain firmly in charge in Tehran.
"With the appointment of the late leader's son as Iran's new leader, US President Donald Trump's goal of regime change in Iran has become more difficult," said Satoru Yoshida, a commodity analyst with Rakuten Securities.
"That view accelerated buying, as Iran is expected to continue its closure of the Strait of Hormuz and attacks on other oil-producing nations' facilities, as seen last week."
The war could leave consumers and businesses worldwide facing weeks or months of higher fuel prices even if the week-old conflict ends quickly, as suppliers grapple with damaged facilities, disrupted logistics and elevated risks to shipping.
"The next flag will be whether it eventually gets to a point where they have to start shutting in oil wells, which not only impacts output even further - it delays a response once the conflict eases as well," ANZ senior commodity strategist Daniel Hynes said.
"That would potentially sustain those prices for much longer."
Iraqi oil production from its main southern oilfields has fallen by 70 per cent to just 1.3 million barrels per day as the country is unable to export oil via the Strait of Hormuz, industry sources said on Sunday.
Crude storage has reached maximum capacity, an official with the state-run Basra Oil Company said.
Kuwait Petroleum Corporation began cutting oil output on Saturday and declared force majeure on shipments, though it did not say how much production it would shut.
