Instead, he said, the convoy had initiated the shooting when a car did not heed a police officer and moved into an intersection.

“The traffic policeman was trying to open the road for them,” he said. “It was a crowded square. But one small car did not stop. It was moving very slowly. They shot against the couple and their child. They started shooting randomly.”

In video shot shortly after the episode, the child appeared to have burned to the mother’s body after the car caught fire, according to an official who saw it.

In interviews on Tuesday, six Iraqis who had been in the area at the time of the shooting, including a man who was wounded and an Iraqi Army soldier who helped rescue people, offered roughly similar versions.

The Iraqi soldier, who said he was standing at a checkpoint on the edge of the square, said he thought the convoy believed the small car was a suicide bomber and opened fire. According to the wounded man, recuperating in Yarmouk Hospital, the car with the family was driving on the wrong side of the road.

The convoy began throwing nonlethal sound bombs, several witnesses said, to keep people in the area away. That drew fire from Iraqi Army soldiers manning watchtowers that are part of an Iraqi Army base on the square. Iraqi police officers, witnesses said, also appeared to be shooting.

The Iraqi soldier, who did not give his name but said he was from a company of Iraqi commandos, said he saw another soldier trying to motion to the convoy to move on, but he was shot as well.