BAGHDAD — As the first armed American drones began flying over Iraq on Thursday, Shiite political leaders were locked in meetings to try to decide who should be the country’s next prime minister. For the first time, some of Prime Minister Nuri Kamal al-Maliki’s own party members expressed doubt that he would be a viable candidate.

Their consultations came against a backdrop of new mayhem from the Sunni-led insurgency that has upended the country and sharpened divisions over whether Mr. Maliki, leader the Shiite-dominated government for seven years, is capable of rescuing Iraq from its worst crisis since the American military left in 2011.

Also, government forces claimed a rare victory over extremists ensconced at a university in the northern city of Tikrit; nine unidentified young men were found shot to death in a town south of Baghdad; and a bomb killed at least 12 people in a Shiite neighborhood of the capital.

And a Pentagon official in Washington said armed Predator drone patrols had started flying over Baghdad, an operation meant to offer added protection to the first American military assessment teams that are fanning out in and around Baghdad to help the Iraqi military combat the insurgents.