However, the defense during Tuesday's hearing left open the likelihood it could seek a hearing on the Florida law before trial begins in June, ABC News reported.
Zimmerman, a Hispanic-American, maintained he shot 17-year-old Trayvon Martin in February 2012 in self-defense, citing the state's stand your ground law. He faces second-degree murder charges for killing Martin. The 29-year-old neighborhood watch volunteer told police he thought Martin was acting suspiciously. Martin's family and supporters said the teen was a victim of racial profiling.
A hearing on the stand your ground law, which had been scheduled for April, could determine whether Zimmerman is entitled to immunity and if he can prove he shot and killed Martin in self-defense. If self defense was determined, all criminal proceedings would stop immediately and Zimmerman would walk.
The two sides also argued over other pretrial issues during Tuesday's hearing, ABC News said.
Zimmerman's defense raised question about the credibility of a teenage girl, identified as Witness 8, who claimed she was on the phone with Martin just before he was shot. She also claimed that after hearing the shooting over Martin's phone, she was hospitalized for trauma, which prosecutors later said was false.
Judge Debra Nelson refused a defense request to question prosecutors about how authorities learned this claim was false, ABC News said. Defense attorney Donald West also asked for more information about the account Witness 8 gave attorneys.
The defense has requested any criminal history police may have on Martin as well as his social media history.
Nelson earlier ruled the defense could subpoena Martin's social media history, which is time-consuming and expensive, ABC News said. Authorities agreed to give the documents to the judge so she could review them and determine if the defense should have them.
"It's time and money to get some of the information here and we are running out of both," West said.