(CNN) -- Florida prosecutors and George Zimmerman's defense attorney want certain evidence -- including e-mails, cell phone records and statements -- sealed until his trial in the death of Trayvon Martin.
Assistant State Attorney Bernie de la Rionda, in a motion filed Thursday, requested a judge seal statements Zimmerman made to law enforcement officers, some of which he called "contradictory."
The prosecutor said some of Zimmerman's statements were "inconsistent with the physical evidence and statements of witnesses."
He did not provide details of the evidence or statements.
The state, citing pretrial publicity, said it wants names and addresses of witnesses kept out of the public record. It asked the same thing for crime scene and autopsy photos, a 911 recording of the incident and cell phone records of Martin, 17. It said those phone records would identify a witness.
Zimmerman's attorney, Mark O'Mara, filed a concurring motion. He said the defense wants 1,000 e-mails received by Sanford police sealed, as well as statements by Zimmerman. He asked that text messages, e-mail messages or journals made by the defendant be kept private, at least until they can be reviewed.
Zimmerman, a neighborhood watch volunteer, is charged with second-degree murder in Martin's February death, which sparked nationwide protests and inflamed public passions over race relations and gun control. Zimmerman has pleaded not guilty.
On a website made on behalf of his client, O'Mara cautioned a rush to judgment since only half of the investigation documents have been made available to the public.
"The remainder of the discovery is currently being scrutinized, and certain information is being properly redacted -- especially information that puts witnesses in potential danger or risks unnecessarily inflaming the cultural tensions that surround this case," O'Mara said on the site. "We agree with the state's decision to attend to this discovery in a methodical, protected way."
A judge will conduct a June 1 hearing on the matter.
CNN's Vivian Kuo contributed to this report.