WASHINGTON—Amid growing signs of instability in Iraq, President Barack Obama authorized a secret plan late last year to aid Iraqi troops in their fight against Sunni extremists by sharing intelligence on the militants' desert encampments, but devoted only a handful of U.S. specialists to the task.

So few aircraft were dedicated to the program, which also faced restrictions by the Iraqis, that U.S. surveillance flights usually took place just once a month, said current and former U.S. officials briefed on the program.

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