Sanford, Florida (CNN) -- After a week of demonstrations nationwide, as well as calls for justice and an uproar over hoodies on Capitol Hill, the focus of the Trayvon Martin saga on Saturday will once again return to the Florida city where it all began.
Thousands of activists are expected to turn out for a Saturday morning march to the headquarters of the Sanford Police Department, whose members have faced extensive criticism for not arresting the 17-year-old Martin's shooter, George Zimmerman.
On February 26, Zimmerman has said, he killed Martin in self-defense in a gated community in that central Florida city. He told police that the teen punched him and slammed his head on the sidewalk before the fatal shooting, according to an Orlando Sentinel report that was later confirmed by Sanford police.
Authorities have said Zimmerman was not immediately charged because there were no grounds, at the outset, to disprove his account that he had acted to protect himself. Yet critics say that Zimmerman, who is Hispanic, deemed Martin "suspicious" and decided to follow him against the advice of a police dispatcher because the teen was black.
That sentiment is expected to be well represented at Saturday's march and subsequent rally. The participants include the president of the Hispanic advocacy group La Raza, teachers union representatives and various NAACP leaders.
Other notables will be the Rev. Jesse Jackson and the Rev. Al Sharpton, both of whom have been regulars throughout the debate and in close contact with Martin's family. The late teenager's parents are not expected to attend.
An open letter on the NAACP's website -- directed at Angela Corey, the special prosecutor assigned to the case -- points to what it calls "evidence of racial bias, investigative mishaps, and the true nature of the circumstances surrounding Trayvon's killing (that) have shaken us to the core...
"However, nothing shakes us more than the knowledge that Trayvon Martin's killer, George Zimmerman, remains free."
The letter ends with a plea for Corey "to prosecute the case judiciously, and to passionately pursue justice."
Sanford Police Chief Bill Lee announced earlier this month that he was stepping down "temporarily" as head of the department amid the public uproar over the shooting. State's Attorney Norman Wolfinger, from Florida's 18th District, also stepped aside in the case.
Gov. Rick Scott has appointed Corey as a special investigator, after which she said that her office could charge Zimmerman, clear him or send the case to the grand jury.
In an interview Thursday with CNN's Piers Morgan, the shooter's brother, Robert Zimmerman Jr., questioned the competence of and the job done by Corey's office thus far.
He cited leaks of details -- which have not been confirmed to have come from Corey or her office -- and described the account that his brother "chased a person" as "absolutely false."
"Ms. Corey's investigation has been compromised," the brother said.
Yet Florida Attorney General Pam Bondi stood staunchly behind Corey, in an interview Friday with CNN's John King. She noted that Scott appointed Corey after consulting with her.
Corey "is ethical. She is honest. She is tough as nails. She is compassionate," Bondi said. "And if any leaks are coming out of this investigation, it is certainly not from Angela Corey's office."
Bondi added that she thought criticism of Corey -- both by those, like Robert Zimmerman Jr., who support George Zimmerman and those calling for his prompt arrest -- "completely undermines the integrity of the investigation."
She said that she's spoken to Martin's parents, whom she called "amazing people," as well as the family's lawyers, whom she described as "friends of mine." Everyone involved, Bondi said, would be best off if they "wait and let (the investigation) happen."
That means being patient in the face of fervent demands from activists that Zimmerman be detained and charged as soon as possible, said the attorney general.
"You never want to make an arrest too soon," Bondi said. "We need justice, but you never want to make an arrest without having all the answers."
While George Zimmerman has not spoken out about the case, his family members have taken their case public this week. Besides the brother, Robert Zimmerman Sr. -- the shooter's father -- told Orlando TV station WOFL that Martin "continued to beat George" and he said something to the effect of, "You're going to die now."
But on CNN Miami affiliate WFOR, Martin's brother Jahvaris Fulton said he finds it "baffling how people ... just take (Zimmerman's) word for it, as if that's exactly what happened." He was especially incredulous about his brother's alleged threat to kill.
"That doesn't sound like my brother at all," said Fulton, a 21-year-old student at Florida International University.
Florida law allows the use of deadly force anywhere a person feels a reasonable fear of death or serious injury. It has been cited in a number of justifiable homicide cases in the state.
But as more information surfaces, the picture of what happened between Martin and Zimmerman becomes more complicated.
Despite the twists and turns, Sybrina Fulton, Martin's mother, has said that she still has faith in authorities investigating her son's case.
"I feel confident that they're going to do a thorough investigation," she said. "We're trying to be patient, even though it's been over a month. We're trying to be patient, and we're trying to press on for justice."
CNN's Umaro Djau, Deirdre Walsh, Ed Payne and Tracy Sabo contributed to this report.