He said he last saw his father on Sunday, when the man stopped by his house to pick up some basketball equipment.
Police planned to give an update later Monday morning on the search for Stephens, who is wanted on a charge of aggravated murder.
The victim's family said they're in disbelief.
Stephens said in the video that he has killed more than a dozen people, police said, though they have said they have found no other victims. That information has not been verified by police. Facebook's live-streaming feature, which was launched in 2010, allows anyone to broadcast online in real time.
This story has been corrected to show the name of the victim is Robert Godwin Sr., not Goodwin.
Employment: Stephens worked for a behavioral health agency, according to the Dayton Daily News.
"We were shocked and horrified to learn of this news today", agency spokeswoman Nancy Kortemeyer said in a statement.
"They rely on the public to flag the content, (saying) 'As soon as you tell us, we'll go take a look, '" he said.
On Sunday, 74-year-old Robert Godwin paid an Easter visit to his son Robert Godwin, Jr. Authorities also said that there had been no evidence that Stephens was in the Philadelphia area. In January, four black people in Chicago were accused of attacking an 18-year-old disabled white man and broadcasting the assault on the service while making anti-white racial taunts.
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During Sunday's vote, about 51.35 per cent backed the constitutional changes, compared to 48.65 per cent for the "no" side. The changes limit any one president to two terms, although under certain circumstances they could seek a third.
As Cleveland police and the Federal Bureau of Investigation were searching for Stephens on Sunday, more than 300 tips poured into the department, police said. Police are warning residents not to approach Stephens if you see him and to call 911. The man claimed to have killed dozens of other people, and police are warning residents in Pennsylvania, New York, Indiana, and MI to be vigilant.
Later identified as Steve Stephens, the man fatally shot Godwin in cold blood, but not before he left a sick message for the world. According to CNN, Stephens then shoots Godwin in the head. He said he wants to kill as many people as possible before being caught.
Williams said police have spoken to the woman that Stephens was referencing and she is safe and cooperating with the probe.
Stephens should be considered armed and unsafe.
Williams said Stephens may be driving a newer model white Ford Fusion, possibly with a temporary license plate.
"He needs to turn himself in so that he can get the help that he needs and he can't keep victimizing this community based on his issues", Williams said. "He is considered armed and unsafe, so we want people to be careful out there", said Cleveland Police Chief Calvin Williams.
Calvin Williams said Sunday that he's urging Steve Stephens to turn himself in and not to "do anymore harm to anybody".
Stephens didn't know his victim and police did not release his motive.