CLEVELAND -- Derrice M. Alexander, 2, was shot and killed by his own father early Tuesday morning, police say.

Police say the incident happened around 5:30 a.m. in the area of 2700 Washington during a domestic dispute between a man and woman.

"The male had a weapon," Deputy Chief Edward Tomba said, at an impromptu press conference outside the scene of the crime.

"He left the residence. Upon leaving the residence, he turned and fired one shot back into the residence, striking the 2-year-old, who was standing on the steps."

The Cuyahoga County Medical Examiner's Office identified the boy as Derrice Alexander Jr., who died at Lutheran Hospital.

Tomba says the father, Derrice M. Alexander, 23, then ran off and went to a relative's home nearby when police were called.

At 4 p.m., Police Chief Calvin Williams held a press conference regarding the incident.

Williams said the department recovered the weapon used and is still in "the process of tracking the weapon" as to where it was obtained. Williams said Alexander has not yet been charged and he is cooperating with police.

Officers responded to Lutheran Hospital for the victim about 5:30 a.m.

The shooting occurred at 2522(B) Division Street where the boy's mother and father engaged in verbal and physical argument.

At some point during the altercation, police say the father was outside and fired a weapon into the window of the residence.

The boy was awake and standing on a landing when he was struck in the head with a single shot.

The father gave the boy to another relative and he was taken by a private car to Lutheran.

Police say the father discarded the weapon into a garbage can in the rear of 2822 Division and then drove off in another car.

Police located him at 1245 W. 45th Street near the Garrett Morgan Water Treatment Plant and had been detained by a Public Utilities Police Officer. The gun was seized.

He was subsequently arrested. "There has been a history of domestic violence at this residence," Tomba says.