BAGHDAD—U.S. commanders say they are unsure about who is responsible for the persistent violence in Iraq, underscoring the challenge they face trying to keep a lid on it amid parliamentary elections this weekend.

While security has improved significantly across Iraq in recent years, in the weeks leading up to the March 7 vote, U.S. commanders have reported an increase in low-level violence: kidnappings, assassinations, and mortar attacks against Baghdad's heavily fortified Green Zone, the seat of government power.

And...