BAGHDAD, March 9 — American soldiers were accused Friday of opening fire on a car carrying a family in the Baghdad district of Sadr City, killing a man and his two young daughters and wounding his son.

The allegations were made by the man’s wife, who was in the car, and members of the Iraqi police, who were at the scene. The American military command said in a statement on Friday that it was investigating an episode in Sadr City involving “an escalation of force,” but it could not confirm any details of the account given by the man’s wife.

The woman, Ikhlas Thulsiqar, said her family had turned from an alleyway onto a main street guarded by American soldiers. Seconds later, she said, a fusillade of bullets ripped into the car.

“They killed the father of my children! The Americans killed my daughters!” she sobbed, sitting crumpled on the floor of Imam Ali Hospital in Sadr City where rescuers had taken the victims, including her daughters, 9 and 11, and her son, 7.