The Islamic State of Iraq and the Levant, a group affiliated with al-Qaida, took control over security checkpoints and other facilities in Fallujah, a restive city in the predominately Sunni province of Anbar.
U.S. combat forces twice took on Fallujah militants at the height of the insurgency that followed the invasion in 2003. U.S. Secretary of State John Kerry said last weekend Washington was willing to support Iraq in its fight against al-Qaida but said there would be no U.S. boots on the ground.
U.S. Sen. Lindsey Graham, R-S.C., told The Daily Beast, a political news website, the U.S. military could supply Apache attack helicopters to help Iraq take on the militants.
"Now is the time to show the Iraqis that even though we don't have troops there, we're supportive of their country," he said in an interview published Wednesday.
"Maliki has got to prove to the world and his people he's not a sectarian leader," Graham said. "He's got to come up with a military strategy with the Sunni tribal leaders to evict al-Qaida."
Maliki, a Shiite, has struggled with Sunni complaints he's marginalizing their community in Iraq.