The Shiite militia groups hold sway around the rich oil fields of southern Iraq, which dominate the country’s oil production, the State Department official said. For that reason, he said, the Shiite militias are more likely to be involved in theft there than the largely Sunni insurgents, who are believed to benefit mostly from smuggling refined products in the north.

In the south, the official said, “There is not an issue of insurgency, per se, but it could be funding Shia factions, and that could very well be true.”

“That would be a concern if they were using smuggling money to blow up American soldiers or kill Sunnis or do anything that could harm the unity of the country,” the official said.

The report by the accountability office is the most comprehensive look yet at faltering American efforts to rebuild Iraq’s oil and electricity sectors. For the analysis of Iraq’s oil production, the accountability office called upon experts at the Energy Information Administration within the United States Department of Energy, which has long experience in analyzing oil production and exports worldwide.

Erik Kreil, an oil expert at the information administration who is familiar with the analysis, said a review of industry figures around the world — exports, refinery figures and other measures — could not account for all the oil that Iraq says it is producing. The administration also took into account how much crude oil was consumed internally, to do things like fuel Iraqi power plants and refine into gasoline and other products.

When all those uses of the oil were taken into consideration, Mr. Kreil said, Iraq’s stated production figures did not add up.

“Either they’re producing less, or they’re producing what they say and the difference is completely unaccounted for in any of the places we think it should go,” Mr. Kreil said. “Either it’s overly optimistic, or it’s unaccounted for.”