"Iran will lose sizeable export volumes, and given Opec+ reluctance to raise output, the market is ill-equipped to fill the supply gap", Harry Tchilinguirian, global head of commodity markets strategy at French bank BNP Paribas, told the Reuters Global Oil Forum.
US officials, including President Donald Trump, are trying to reassure consumers and investors that enough supply will remain in the oil market and have pushed OPEC to raise output.
On Tuesday, Mr. Trump's address to the world body is expected to focus heavily on Iran and the threat he says the Islamic Republic poses to Middle Eastern stability through its support for proxy forces in Syria, Lebanon and elsewhere.
Mr. Rouhani also did not rule out talks, but a change in US policy will be needed first.
Oil prices eased on Wednesday after US data showed a surprise build in domestic crude inventories, but an impending drop in Iranian exports kept Brent futures above $80 a barrel and on track for a fifth straight quarterly gain.
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If U.S. President Donald Trump wants the price of oil to stop going up, he should stop interfering in the Middle East, Iranian oil minister Bijan Zanganeh said on Wednesday, according to the Iranian Students' News Agency (ISNA).
Oil prices jumped more than two per cent to a four-year high on Monday after Saudi Arabia and Russian Federation ruled out any immediate increase in production.
The WTI Crude Oil market rallied during trading on Tuesday, but it seems to be struggling with the idea of $73 a barrel.
Opec members do not have the capacity to increase production, Zanganeh said. Eventually, I do believe that the market will be used to that price and we will be able to go higher, but we may be a little bit overextended over the last couple of days.
Most of the potential supply shortfall has already been priced into the contract, Again Capital's Kilduff said.
It said crude oil and condensates exports were 2.8 mbd in April and are now estimated at 2.0 mbd in September.