BAGHDAD — On a good day, the drive from Falluja to Baghdad takes less than an hour. On Sunday morning, with his city under siege, its morgue filled with bodies and people running low on food, water and generator fuel, Osama al-Ani packed his family of seven into his car and set off for the capital. The trip, with its constant checkpoints and vehicle searches, took more than 12 hours, he said.

Yet, even after being forced to flee for his family’s safety, Mr. Ani remains more sympathetic to the militants who have set up checkpoints across his city and are largely aligned with Al Qaeda than he is toward the central government.

“We had no food, no electricity and no water, and mortar shells were falling all around us,” said Mr. Ani, who is staying with relatives in the Sunni neighborhood of Ameriya here. “But many of us would rather support Al Qaeda than the army that has led to this massacre.”

Sunni militants, some members of the Qaeda-affiliated Islamic State of Iraq and Syria, or ISIS, and some armed tribesmen angry with the government set off days of fighting when they took control of Falluja last week. On Tuesday fierce clashes erupted again, while government forces with tanks and heavy weapons circled the city, waiting for orders from the prime minister. In Baghdad, officials held off calling for an offensive, heeding pleas from local leaders inside Anbar who warned that civilian casualties would end any amount of support the government could count on from local tribes in routing Al Qaeda.