Russia has targeted Syrian rebel groups backed by the Central Intelligence Agency in a string of airstrikes running for days, leading the U.S. to conclude that it is an intentional effort by Moscow, American officials said.

The assessment, which is shared by commanders on the ground, has deepened U.S. anger at Moscow and sparked a debate within the administration over how the U.S. can come to the aid of its proxy forces without getting sucked deeper into a proxy war that President Barack Obama says he doesn’t want. The White...