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|File photo of section of an oil platform in the North Sea, around 160 kilometres east of Aberdeen, Scotland. (AFP PHOTO/POOL/ANDY BUCHANAN)|
The main crude futures contracts had already been rising in recent weeks, hitting 3.5-year highs, on expectations Trump was going to withdraw from the 2015 pact that had opened up Tehran's atomic programme in return for an easing of sanctions.
On Wednesday, they each gained nearly three per cent.
"The geopolitical repercussions of this decision will no doubt be widely felt, and due to as many as one million barrels of crude supply per day being effectively taken off the market," said David Cheetham, chief market analyst at traders XTB.
Trump's decision alone was unlikely to have a major impact on the world's oil supply, said Thomas Pugh, commodities economist at Capital Economics.
"However, geopolitical tensions have intensified and if Iran decides to pull out of the nuclear deal, the impact on oil supply could be more severe," he said, predicting that oil prices would probably "remain elevated for the next few months at least".
A surprise fall in last week's oil stocks in the US, reported on Wednesday, added to upward pressure on oil contracts. Analysts had expected crude inventories to show an increase.
"Traders believe the sanctions will further tighten global supply at a time when some of the world's largest producers have already significantly reduced inventories," said Craig Erlam, an analyst with OANDA.
Oil's surge in turn helped lift shares prices in energy majors, with Royal Dutch Shell and BP higher in London.
"Both these firms have seen their share price rise to its highest level in several years," said Cheetham.
Wall Street rose as New York-listed energy stocks, including ExxonMobil and Chevron, were up sharply.
Saudi Arabia, the world's largest oil exporter, has meanwhile said it will take all necessary measures to prevent supply shortages.
Trump reinstated US sanctions which could curtail Iran's ability to export oil, its mainstay for public revenues.
In an initial reaction to Trump's announcement on Tuesday Brent and WTI eased back, with some commentators suggesting he could still pedal back on some of his rhetoric and shift to a more diplomatic tone.
But when that did not happen they bounced back strongly.
There is now talk that crude could rise to US$80 a barrel, with gains helped also by uncertainty in oil-rich Venezuela, an OPEC-Russia output cap, improving global demand and a drop in US energy stockpiles.
Key figures around 1535 GMT:
Oil - Brent North Sea: UP US$2.17 at US$77.02 per barrel
Oil - West Texas Intermediate: UP US$1.91 at US$70.97 per barrel
London - FTSE 100: UP 1.3 per cent at 7,662.52 points (close)
Frankfurt - DAX 30: UP 0.2 per cent at 12,943.06 (close)
Paris - CAC 40: UP 0.2 per cent at 5,534.63 (close)
EURO STOXX 50: UP 0.3 per cent at 3,569.99
New York - Dow: UP 0.1 per cent at 24,371.30
Tokyo - Nikkei 225: DOWN 0.4 per cent at 22,408.88 (close)
Hong Kong - Hang Seng: UP 0.4 per cent at 30,536.14 (close)
Shanghai - Composite: DOWN 0.1 per cent at 3,159.15 (close)
Euro/dollar: DOWN at US$1.1859 from US$1.1864 at 2100 GMT
Pound/dollar: UP at US$1.3581 from US$1.3548
Dollar/yen: UP at 109.73 yen from 109.07 yen