The jurors reported its impasse on Wednesday, after only about two and a half hours of deliberations that began Tuesday afternoon.
They are stuck trying to decide whether Arias should be sentenced to life in prison or death for killing her one-time boyfriend, Travis Alexander. The judge instructed them to continue deliberations and try to work through their differences by identifying areas of agreement and disagreement as they work toward a decision.
Under Arizona law, a hung jury in the death penalty phase of a trial requires a new jury to be seated to decide the punishment. If the second jury cannot reach a unanimous decision, the judge would then sentence Arias to spend her entire life in prison or be eligible for release after 25 years.
Earlier Wednesday, jurors were called to the courtroom for a clarification of their instructions.
The judge had already explained that the jury's decision would be final and wasn't just a recommendation. However, she did not clarify that a life sentence could mean Arias would be eligible for release after 25 years or spend her remaining days behind bars, and that decision would be up to the judge.
About an hour later, the jury informed the court it was unable to reach a decision.
If jurors ultimately cannot agree on a sentence, the case could drag on for several more months, said former Maricopa County Attorney Rick Romley. Romley said that with the second jury, the guilt finding would still stand, and the new panel would be considering only the sentence.
However, Romley added that the new jury would have to review evidence and hear opening statements, closing arguments and witness testimony in a "Cliffs Notes" version of the trial. He said there are no limitations in the law to restrict just how long attorneys have to present their cases again before the panel attempts to reach a decision.
Romley also noted that if the current jury deadlocks, the prosecutor could decide to take the death penalty off the table. If that happens, the judge would decide whether Arias spends her entire life in prison or is eligible for release after 25 years. The judge cannot sentence Arias to death.
The current jury of eight men and four women convicted Arias of first-degree murder two weeks ago. Arias stabbed and slashed Alexander about 30 times, shot him in the forehead and slit his throat in what authorities said was a jealous rage. Arias claimed it was self-defense.
After the conviction, Arias told a local TV station that she preferred the death penalty. However, she said Tuesday night that she changed her mind after a tearful meeting with family members, realizing her death would only cause them more pain.
The Associated Press contributed to this report.