"At the moment oil production isn't affected," Dudley said on the sidelines of an energy conference in Moscow.
"I don't believe that this kind of difficulty and instability will spread all the way to the far south of Iraq" -- home to the majority of the country's oil operations.
"But we should all be very alarmed by what is happening," Dudley told reporters at the World Petroleum Congress.
The United States is deploying extra troops to protect its embassy in Baghdad and mulling air strikes against Islamist fighters who have seized key cities.
Militants who seized Mosul -- a city of two million people -- and then a vast swathe of territory north of Baghdad in a lightning offensive launched eight days ago, are making further advances, Iraqi officials said.
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"At the moment, the implications for oil production appear limited," Dudley added.
"The majority of oil production is located in the south, it is a long way from the troubles."
BP has so far removed only non-essential staff from Iraq, which produces about 3.5 million barrels of oil per day.
While most of Iraq's oil and gas fields are in the centre and the south of the country, militants have seized territory in Iraq's oil-producing Kirkuk province.
BP, meanwhile, is part of a consortium that is hoping to significantly increase outpout at the giant Rumaila oil field in southern Iraq.