(CNN) -- A solemn George Zimmerman, wearing gray jail coveralls, appeared before a Seminole County, Florida, judge Thursday, speaking only a few words as his arraignment was set for next month.
All matters including bond and further motions in the case will be handled by the circuit court, Judge Mark Herr said. The case will be assigned to Judge Jessica Recksiedler going forward.
As the short hearing was concluding, Zimmerman's attorney, Mark O'Mara, asked that records containing personal information on witnesses, including addresses and telephone numbers in some cases, be sealed. As nothing else besides the probable cause affidavit had been filed in court Thursday, Herr said Recksiedler will address a motion to seal the file.
O'Mara did not ask that Zimmerman be released on bond, although he said earlier in the day he wanted his client released as soon as possible.
He did note, however, that being out on bail could jeopardize Zimmerman's safety.
"I think nobody would deny the fact if George Zimmerman is walking down the street today, he would be at risk," he explained.
O'Mara said earlier Thursday he is "truly hoping that there will be a receding of the frustrations or anger now that the process is moving forward."
Zimmerman, 28, who had been in hiding, turned himself in Wednesday after authorities said he would be charged in the case. He faces a second-degree murder charge in the February 26 shooting death of 17-year-old Trayvon Martin.
The development marks a turning point in a case that triggered a nationwide debate about race in America and about Florida's "stand your ground" law -- which allows people to use deadly force anywhere they feel a reasonable threat of death or serious injury.
O'Mara said Zimmerman, who will plead not guilty at his arraignment, is worried about getting a fair trial in Sanford -- where thousands have converged to join in protests calling for his arrest and decrying the police department's handling of the case.
But O'Mara said he does not share those concerns.
"Florida has a very good process in place to make sure we get a fair and impartial jury," he told CNN. "Other high-profile cases have been able to do so. I trust that the system, the judge, the prosecutor and I will be able to, should the need arise, to get ourselves a fair and impartial jury to hear the case. It may not be in Seminole County."
Martin's family, meanwhile, expressed satisfaction that Zimmerman has been charged and is in custody.
"We simply wanted an arrest; we wanted nothing more, nothing less," the teen's mother, Sybrina Fulton, said Wednesday.
Natalie Jackson, an attorney for Martin's family, said Thursday the family has only asked "for justice to apply equally for all. If a judge decides (Zimmerman) has a right to bail, then that's the system, and we'll respect the system."
On Thursday, Fulton released a statement clarifying comments she made earlier on NBC's "Today."
"I made a comment to the media that was later mischaracterized," she said. "When I referenced the word 'accident' today with regard to Trayvon's death, in no way did I mean the shooting was an accident.
"We believe that George Zimmerman stalked my son and murdered him in cold blood," Fulton said. "The 'accident' I was referring to was the fact that George Zimmerman and my son ever crossed paths. It was an accidental encounter. If George Zimmerman hadn't gotten out of his vehicle, this entire incident would have been avoided.
"My son was profiled, followed and murdered by George Zimmerman, and there was nothing accidental about that," she said.
Earlier, Fulton told NBC, "I believe it was an accident. I believe that it just got out of control, and he couldn't turn the clock back."
She told "Today," "I would ask (Zimmerman), did he know that that was a minor, that he was a teenager and that he did not have a weapon? ... I understand that his family is hurting, but think about our family that lost our teenage son."
Why second-degree murder
The special prosecutor assigned to the case announced the charge against Zimmerman Wednesday -- 46 days after the shooting.
During that time, the calls for "Justice for Trayvon" had grown louder and louder, with Martin's supporters taking to the streets in cities across the nation and on the Internet.
Prosecutor Angela Corey said whether the case is decided by a judge or jury, "I can assure they will only get the relevant, admissible evidence on which they can then base their decisions."
"Let me emphasize that we do not prosecute by pressure or petition. We prosecute cases based on the relevant fact of each case and on the laws of the state of Florida," said Corey, who has a reputation for taking on tough, controversial cases in the three counties that make up the 4th Judicial Circuit.
Prosecutors usually level a second-degree murder charge when they accuse someone of a killing that is not premeditated or planned. It carries a maximum sentence of life