Police said seven died on Saturday while the military said three.
"The driver ignored verbal warning and several warning shots," the military said in a statement.
"As US marines in the vicinity of the checkpoint attempted to disable the van, the van accelerated toward the marines. The marines then fired upon the vehicle to protect themselves and the integrity of the checkpoint."
Ramadi police chief Brigadier Jasim al-Dulaimi said seven died in the shooting near the central governorate building where US troops are positioned.
Reuters Television footage showed the bus peppered with bullet holes. Some of the windows were shattered and others spattered with blood.
Flies buzzed around corpses in the vehicle, as men carried away bodies and loaded them into cars.
Also in Ramadi, armed men ambushed a convoy of Iraqi national guardsmen on Sunday, killing nine and wounding 17, local hospital officials said.
The rocket-wielding fighters ordered the guards from their vehicles and then gunned them down after holding them up on a main street in broad daylight and forcing them to drive to the outskirts of the city, wounded survivors said.
The attackers then torched the guards' two trucks.
In Samarra, another mainly Sunni city north of Baghdad, three Iraqis were killed and six others wounded in fierce clashes between fighters and US troops, medical sources said.
Following the clashes, which erupted last night and continued into the morning, a joint force comprising US and Iraqi troops arrested a number of citizens.