BAGHDAD — The United States has conducted an escalating campaign of deadly airstrikes against the extremists of the Islamic State for more than a month. But that appears to have done little to tamp down the conspiracy theories still circulating from the streets of Baghdad to the highest levels of Iraqi government that the C.I.A. is secretly behind the same extremists that it is now attacking.

“We know about who made Daesh,” said Bahaa al-Araji, a deputy prime minister, using an Arabic shorthand for the Islamic State on Saturday at a demonstration called by the Shiite cleric Moktada al-Sadr to warn against the possible deployment of American ground troops. Mr. Sadr publicly blamed the C.I.A. for creating the Islamic State in a speech last week, and interviews suggested that most of the few thousand people at the demonstration, including dozens of members of Parliament, subscribed to the same theory. (Mr. Sadr is considered close to Iran, and the theory is popular there as well.)

When an American journalist asked Mr. Araji to clarify if he blamed the C.I.A. for the Islamic State, he retreated: “I don’t know. I am one of the poor people,” he said, speaking fluent English and quickly stepping back toward the open door of a chauffeur-driven SUV. “But we fear very much. Thank you!”

The prevalence of the theory in the streets underscored the deep suspicions of the American military’s return to Iraq more than a decade after its invasion, in 2003. The casual endorsement by a senior official, though, was also a pointed reminder that the new Iraqi government may be an awkward partner for the American-led campaign to drive out the extremists.