Hinds County Circuit Judge Winston Kidd says he'll decide by Friday whether to further extend his June 28 order that blocked the law from taking effect July 1.
Kidd heard arguments Monday from plaintiffs who sued to stop the law and a state attorney who defended it.
Plaintiffs' attorney Lisa Ross calls the law unconstitutionally vague.
Assistant Attorney General Harold Pizzetta says plaintiffs are trying to make the law confusing.
Earlier this year, legislators passed and Gov. Phil Bryant signed House Bill 2, which says adults don't need a permit to carry a gun that's not concealed.
Bryant's spokesman Monday said there's no chance the governor will call a special session to clarify the law.