The most-active December Brent crude futures contract LCOv1 settled up 59 cents at $81.38 a barrel, below the session high of $81.90 but still within sight of Tuesday's four-year high of $82.55.
Brent has risen by around 20 percent from the most recent lows in August.
Futures were little changed in NY after closing Monday at the highest since November 2014.
The message was delivered by Ali Kardor, the head of state-run National Iranian Oil Company, who added that his country's oil income has increased 40 percent in the past year and that it may start offering oil via its stock exchange as soon as next week - which would allow private companies to export, thus bypassing the USA sanctions.More news: Police Chief 'Heartbroken' After Body Discovered in Creek
State oil giant Saudi Aramco is expected to pick up an additional 550,000 bpd of oil production capacity from two major oil fields in the fourth quarter, so it would be able to increase production if there's demand, said a report.
"The market's very keen to figure out the size of impact from the Iranian supply disruptions and whether Saudi Arabia and Russian Federation are able to make up for the losses", Kim Kwangrae, a commodities analyst at Samsung Futures Inc., said by phone.
That comes as the overall supply of oil looks set to decline, post United States sanctions against Iran and despite increases from Russian Federation and Saudi Arabia. "This increases the growth prospects not only for Canada and the USA, but for North America as a whole". An oil analyst has said crude prices will touch $100 per barrel as producers have no means to stop such a spiral - something not seen since 2014.
Head of trading for Asia-Pacific at futures brokerage in Singapore Stephen Innes said even if Saudi Arabia, wanted to grant Trump's wishes, it is uncertain how much spare capacity the kingdom has.
With crude prices soaring and many currencies in emerging markets, including India's rupee and Indonesia's rupiah declining, analysts warn that economic growth may be eroded.