The price of a barrel of Brent crude for delivery next month rose to more than $120 on Monday.
On Sunday, the country’s oil ministry said it had halted oil sales to British and French companies ahead of the imposition of EU sanctions in July.
Iran is the world’s fifth-largest oil exporter.
Iran insists its nuclear programme is peaceful, but the UN’s International Atomic Energy Agency says it has information suggesting Iran has carried out tests “relevant to the development of a nuclear explosive device”.
Analysts say the price of oil has risen as EU countries seek to find new oil suppliers and Iran hunts new buyers for its oil.
“The increase in price is a direct result of European importers of Iranian oil looking round to find alternative sources,” said Professor Paul Stevens from Chatham House.
Oil prices have also been driven up by an improvement in the performance of the US and Chinese economies.
The US is the world’s largest consumer of oil.
“It’s been a combination of a couple of factors, obviously geo-political tensions are rising, especially Iran,” said Amrita Sen, an oil analyst at Barclays capital.
“But the price support has also come through, because fundamentals have tightened up.”
Factors include stronger demand because of Asian growth and the European cold spell. At the same time, supply from South Sudan and Syria to Europe has also been cut.
If there is no further tension in Iran, the oil price may fall back. However, few analysts think this is likely.
“That assumes that Iran doesn’t do anything else, but that is a doubtful assumption,” added Prof Stevens.
“If there was a military attack on Iran, then all bets are off.”