In a statement Sunday evening from publicist Lisa Kasteler, Jennifer Hudson appealed to the public for its help, offering the reward and asking that any information be given to Chicago police.
"Jennifer and her family appreciate the enormous amount of love, support and prayers they have received while she and her family try to cope with this tragedy and continue the search for Julian," the statement said.
Chicago police ramped up search efforts for Julian around the Englewood neighborhood, where Hudson grew up, and transferred custody of a "person of interest" in the killings to state authorities.
"Detectives are working 24 hours on this case," said Chicago police spokeswoman Monique Bond. "There's a lot of forensic evidence. We have to work the evidence and try and solve this case. Most importantly, we want to find the child."
An Amber Alert remained in effect Sunday for Julian, who disappeared on Friday, the day the bodies of his grandmother, Darnell Donerson, 57, and 29-year-old uncle Jason Hudson were found in the home they all shared on the city's South Side. The deaths were ruled homicides.
The Amber Alert listed William Balfour, the estranged husband of Jennifer Hudson's sister, Julia Hudson, as a suspect in a "double homicide investigation."
Authorities said the search for Julian would be citywide, but on Sunday residents and officers focused their efforts "in the immediate vicinity" of the home, said police spokesman Dan O'Brien.
Police said they did not have a motive for the killings but called the case "domestic related." Bond said Balfour had not been charged.
"There's a lot of forensic evidence. We have to work the evidence and try and solve this case," Bond said Sunday. "Most importantly, we want to find the child."
Bond said no weapon had been found at the Hudson home, a three-story house sandwiched by vacant lots littered with trash. Investigators on Sunday moved in and out of the home and examined the trash.
Mourners stopped by the Hudson home, many laying teddy bears along the chain link fence around the property. Others signed a cross that rested on the fence.
"We love you," one message read. Another said, "We'll find the people who did this."
Police officers were instructed to place fliers with Julian King's picture and description in every business in the area.
Jennifer Hudson, who won an Academy Award for best supporting actress in 2007 for her role in "Dreamgirls," was in Chicago with her family during the weekend, her sister said. Her publicist did not disclose her whereabouts, but the Cook County medical examiner's office confirmed she had identifed the bodies of her mother and brother.
Bond said Balfour, who had been in police custody since Friday, was transferred Sunday to the Illinois Department of Corrections "based on his active parole violation unrelated to this investigation."
Records from the corrections department show Balfour, 27, is on parole and spent nearly seven years in prison for attempted murder, vehicular hijacking and possessing a stolen vehicle.
Corrections spokeswoman Januari Smith said Balfour would likely remain in state custody until the Illinois Prisoner Review Board looked at his case. She would not say exactly where Balfour was being held.
It was unclear whether Balfour had an attorney Sunday, but his mother, Michele Balfour, has denied he was involved the killings or in Julian's disappearance.
In a MySpace blog entry on Sunday, Hudson said she was grateful for community support and posted a picture of her sister's son.
"Thank you all for your prayers and your calls," she wrote. "Please keep praying for our family and that we get Julian King back home safely."