When asked by CNBC if the multinational oil giant was in dialog with the Middle Eastern nation, Dudley said Wednesday: "We are not in any discussions with Iran. It (BP) is a company that was founded over 100 years ago in Iran, but we do not do business with Iran today."
Dudley was speaking to CNBC from the World Economic Forum in Davos , Switzerland. Economic and political policymakers, as well as corporate executives, attend the annual meeting.
Dudley was appointed executive director of BP in 2009, after joining the company following its merger with Amoco.
Regarding the decision of Iranian President Hassan Rouhani to attend Davos, Dudley said: "I think dialog is great. It is the heart of developing policy and decisions."
Iran struck a six-month interim deal with the UN Security Council, which took effect on Monday. The country agreed to limit its nuclear enrichment program in exchange for certain international sanctions being lifted.
While Iran is still only allowed to sell 1 million barrels per day of crude oil, a successful deal could see a long-term pact being struck, with all sanctions - including those on oil sales - being lifted.
(View more: Iranian oil won't reach market in 2014: Pro)
Analysts see a long-term deal with Iran as likely to bring down global oil prices.
"That event, in conjunction with other possible supply increases, means that at the end of 2014 we could be in a situation where the oil price is under serious downward pressure," Neil Atkinson, head of analysis at Lloyd's List Intelligence, told CNBC last week.
(Read more: Fishermen sue Texas lawyer in BP claims dispute)
The price of crude oil rose to $96.28 per barrel on Wednesday, boosted by hopes that improving international economic climes will lead to higher energy demand.
Oil prices were also lifted by the possibility of supply disruption in Libya, where five government ministers, including the oil minister, have recently resigned.
image: © Mark Morgan