Chicago (CNN) -- Prosecutors said Tuesday the career criminal accused of killing a 6-month-old Chicago girl admitted to other people that he shot into the van where Jonylah Watkins was sitting on her father's lap in March.
Before Koman Willis' bond hearing was postponed until June 6, Assistant State's Attorney Heather Kent said his cell phone and his girlfriend's minivan could be traced to the area at the time of the killing through phone records and surveillance video.
She claimed there was at least one unidentified witness who stepped forward and said that Willis admitted to the March 11 shooting.
According to court documents, Willis saw Jonathan Watkins, Jonylah's father. Suspecting that Watkins had stolen a Sony PlayStation system and drugs from the home of his mother, Willis went to get a gun, the documents say. Willis drove a van to the alley where Watkins was parked and changing Jonylah's diaper; he walked up behind the van and fired four shots, the documents say.
Prosecutors say Willis began firing as Watkins lifted his baby up to give her a kiss. Jonylah, whose death was held up nationally as a new low in Chicago's gun violence, passed away the next day.
After the shooting, Willis parked the van in a garage and removed the plates.
Lawyers ask for more time
On Tuesday, his lawyers said they needed more time to prepare their case.
Willis, 33, is charged with first-degree murder and aggravated battery with a firearm.
In announcing Willis' arrest on Monday, Chicago police superintendent Garry McCarthy said the suspect is a gang member with 38 prior arrests.
Kent said Tuesday that Willis' extensive criminal record includes a 2002 arrest for aggravated assault to a police officer for which he served a three-year prison sentence. He also had been charged several times for felony drug possession.
Willis turned himself in Saturday afternoon. He came in with an attorney because he knew police were looking for him, McCarthy said.
The superintendent said this was not a case of gang violence even though the suspect and the victim's father have ties to gangs.
"We believe the motivation was the burglary," he said. He said it was unlikely Watkins, 29, will be charged with theft.
Lead investigator Kevin Duffin said police were able to identify new witnesses last week.
"They provided some key information that got the ball rolling," he said.
No weapon or getaway van has been recovered, police said. McCarthy said "we're still not at that point" to say that Willis acted alone, but no other charges are expected soon.
Father says he has become a new man
Jonathan Watkins, who was seriously wounded in the shooting, told reporters Tuesday, that he has changed his life since his daughter died.
He said he goes to church now and has a real job.
"I don't stand on the corners no more," he said. "I'm just a whole different person now."
He said he won't go back to a life of crime.
"I know my baby out there is looking down on me," he said. "I can't change (and go back to selling drugs)."
He said he had never met Willis but refused to answer any other questions about the case.
"I feel better that somebody's been caught," he said.
Despite police assertions that he was a gang member, Watkins said he hasn't be in a gang since he was a teenager.
When pressed about the burglary of the video game system, he turned to Pastor Corey Brooks, who said Willis' trial would be the time for the details to be revealed.
"But we can assure you that there is more to it than what's being said," said Brooks, the pastor of New Beginnings Church of Chicago.
He added that he has taken Watkins under his wing to make sure he doesn't return to a life where crime is the only means he has of supporting himself.
CNN's Ted Rowlands and Carma Hassan contributed to this story.