BAIJI, Iraq — On the front lines of the battle against the Islamic State, suspicion of the United States runs deep. Iraqi fighters say they have all seen the videos purportedly showing U.S. helicopters airdropping weapons to the militants, and many claim they have friends and relatives who have witnessed similar instances of collusion.

Ordinary people also have seen the videos, heard the stories and reached the same conclusion — one that might seem absurd to Americans but is widely believed among Iraqis — that the United States is supporting the Islamic State for a variety of pernicious reasons that have to do with asserting U.S. control over Iraq, the wider Middle East and, perhaps, its oil.

“It is not in doubt,” said Mustafa Saadi, who says his friend saw U.S. helicopters delivering bottled water to Islamic State positions. He is a commander in one of the Shiite militias that last month helped push the militants out of the oil refinery near Baiji in northern Iraq alongside the Iraqi army.

The Islamic State is “almost finished,” he said. “They are weak. If only America would stop supporting them, we could defeat them in days.”

U.S. military officials say the charges are too far-fetched to merit a response. “It’s beyond ridiculous,” said Col. Steve Warren, the military’s Baghdad-based spokesman. “There’s clearly no one in the West who buys it, but unfortunately, this is something that a segment of the Iraqi population believes.”

The perception among Iraqis that the United States is somehow in cahoots with the militants it claims to be fighting appears, however, to be widespread across the country’s Sunni-Shiite sectarian divide, and it speaks to more than just the troubling legacy of mistrust that has clouded the United States’ relationship with Iraq since the 2003 invasion and the subsequent withdrawal eight years later.

At a time when attacks by the Islamic State in Paris and elsewhere have intensified calls for tougher action on the ground, such is the level of suspicion with which the United States is viewed in Iraq that it is unclear whether the Obama administration would be able to significantly escalate its involvement even if it wanted to.

“What influence can we have if they think we are supporting the terrorists?” asked Kirk Sowell, an analyst based in neighboring Jordan who publishes the newsletter Inside Iraqi Politics.

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