Uncertainty surrounding Iran's oil industry ahead of forthcoming U.S. sanctions could prompt "extreme volatility" for oil prices, BP's chief executive told CNBC Wednesday. "I think it's going to be 45 days of extreme volatility, it could spike up, it could also go the other way," he told CNBC's Steve Sedgwick in London. Dudley's comments come at a time when oil market players are closely watching what happens when U.S. sanctions on Iran's oil industry come into force on November 4. It's hard to be precise over how much of Iran's production will be affected by the sanctions. It largely depends on whether the country's oil-buying customers are afraid of secondary sanctions from the U.S. if they do business with Iran. BP's competitor Total announced in August that it was pulling out of a giant oil and gas project in the Islamic republic. But BP and Serica Energy were granted a new license Tuesday to run a North Sea gas field partly owned by Iran showing the U.S. is willing to make some exemptions to the reach of the sanctions.

BP CEO Bob Dudley pauses during a news conference at the company's headquarters in London. Jason Alden | Bloomberg | Getty Images

"If waivers were granted to others, to big oil consuming countries, you could see it (the price) go down, there's a lot of uncertainty right now," Dudley said. Some analysts predict as much as 1.5 million barrels per day could be removed from the market, an event that could cause prices to rise further. On Wednesday, Brent crude futures were trading at $84.96 per barrel while U.S. West Texas Intermediate was trading at $74.92.

No fall in demand