Under the measure offered by state Senate Minority Leader Chris Smith, D-Fort Lauderdale, Floridians would not be able to automatically cite the self-defense law if they provoke or pursue their assailant following a confrontation, The Palm Beach Post reported.
His bill also would allow law enforcement officers to arrest anyone who invokes the "stand your ground" law under questionable circumstances, the newspaper said.
"These common sense changes are not about taking away gun rights from Floridians," Smith said in a statement. "It's about stemming the culture of violence in our society by putting responsibility for the consequences back into the hands of gun users, and anyone who deploys deadly force under stand your ground."
Smith introduced the bill in response to the Trayvon Martin case, in which the unarmed 17-year-old was shot to death early this year by neighborhood watch volunteer George Zimmerman, 29, in Sanford.
Currently in Florida, authorities can't arrest someone who invokes the statute unless there is probable cause to believe their actions were unlawful. Smith said the law is unclear on whether the law covers those who pursue their assailant.
The Post said Smith's bill will likely find tough sledding in the Republican-controlled Legislature.
Guns aren't the only weapons involved in "stand your ground" cases. The Orlando Sentinel reported the presiding judge in the Zimmerman murder case Wednesday rejected the self-defense claim of a Casselberry man arrested for hitting a neighbor with a shovel.
James Fraleigh, 54, contended in court last week he was legally standing his ground when he hit Dylan Wells, 21, during a Jan. 7 dispute over the fence separating their homes, inflicting a gash on the back of his neck. Wells was not seriously hurt.
Fraleigh said he only swung the shovel after Wells lowered his head and charged at him, hitting him below the waist. Fraleigh said was afraid he was about to suffer a serious injury.
But Circuit Judge Debra Nelson decided Fraleigh was the aggressor.