SANFORD, Florida (CNN) -- Civil rights luminaries joined throngs of protesters carrying "Justice for Trayvon" signs on Saturday, slowly marching to the Sanford police headquarters to demand the arrest of 17-year-old Trayvon Martin's killer.
"We will march on, we will rally, pray, petition, challenge elected officials, judges, law enforcement, attorneys, in the court house and in the White House, until justice for Trayvon Martin is real," high school senior Clarence Moore III, a member of the NAACP's College and Youth Division.
Roslyn Brock, chairwoman of the NAACP board of directors, urged demonstrators to turn their anger into constructive action, telling them to register and vote.
"Your vote is the key that will unlock justice in this community," she said.
Organizers said demonstrators arrived on buses from around Florida and the Southeast to participate in the rally, which came 34 days after neighborhood watch volunteer George Zimmerman fatally shot Martin after calling police to report him as a "suspicious" person.
Zimmerman says he killed Martin in self-defense after the teen punched him and slammed his head on the sidewalk, 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'd acted to protect himself. Martin's family and supporters say Zimmerman, who is Hispanic, racially profiled the teen, who was black, and ignored a police dispatcher's directive not to follow him.
The Sanford police department has come under intense scrutiny for its actions following the shooting, and protesters renewed their call for the firing of police Chief Bill Lee, who stepped aside temporarily this month amid criticism. Activists also demand punishment against others involved in the case.
"The same thing that happened to Trayvon Martin can happen to your kids as well," said Seminole County NAACP President Turner Clayton. "We want a clean house at Sanford P.D."
Civil rights figures, including the Rev. Jesse Jackson, the Rev. Al Sharpton, NAACP President Ben Jealous and others joined the marchers at the rally, saying the incident was only the latest in a long string of incidents with black men, particularly, as victims of racially motivated crimes.
As he has in recent days, Jackson said that Martin's killing is symptomatic in part of the larger problem of violence in the United States. Yet he also said he believes that the teenager's skin color contributed to his death.
"This is about race profiling, and therefore a quest for racial justice," said Jackson, who added later, "It's hope time, it's healing time."
At a news conference that preceded the march, Jealous and Sharpton took pains to rebut reports that Sharpton's National Action Network was considering calling for a boycott of Sanford or Seminole County.
Sharpton said such a boycott was "never on the table." But he said he would consider action against businesses supporting efforts on behalf of Florida's "stand your ground" law, which police have cited as a reason they did not immediately arrest Zimmerman.
The law allows people to use deadly force anywhere they feel a reasonable threat of death or serious injury. Critics say it is a "shoot first" law that justifies violence.
A special prosecutor appointed by Gov. Rick Scott is investigating the case, as is the U.S. Department of Justice.
An open letter on the NAACP's website -- directed at the special prosecutor, Angela Corey -- 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."
In an interview Thursday with CNN's Piers Morgan, the shooter's brother, Robert Zimmerman Jr., questioned 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.
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."
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 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.