Defense attorney Mark O'Mara asked that the witnesses be allowed to testify out of the public eye because of concerns for their safety about testifying at the trial, which starts next week. He said their testimony could impact the jury's decision.
Prosecutors and attorneys for media groups objected to the request.
Circuit Judge Debra Nelson also heard testimony about whether a voice recognition expert will be allowed to testify at the trial. Cries for help can be heard in the background of 911 calls that Zimmerman's neighbors made during a struggle between the neighborhood watch volunteer and Martin before the unarmed teen was shot. Experts have reached mixed conclusions about whose voice is crying for help.
FBI voice expert Hirotaka Nakasone, who was testifying for the defense, said there wasn't enough clear sound on the 911 recording to determine whose voice it was. He also said the concept that individuals have unique voice-prints that could identify them was misleading.
"No one can speak in the same way twice," Nakasone said.
Testimony was to continue Friday and the judge didn't issue a ruling.
Zimmerman has pleaded not guilty to second-degree murder, claiming self-defense, in the racially charged case. A delay in Zimmerman's arrest led to protests nationwide. Martin was black. Zimmerman's father is white, and his mother is Hispanic.
The trial is expected to last more than a month.
The judge also considered a request from defense attorneys to sanction prosecutors for what the defense said amounts to withholding evidence. Zimmerman's attorneys alleged that prosecutors withheld deleted photos and text messages that came from Martin's cellphone. An attorney for a technology worker in the State Attorney's Office testified that he first brought the evidence to the attention of Zimmerman's attorneys after he was contacted by the technology worker.
The judge decided to suspend further testimony on sanctions, and any decision, until after the trial.