Hossein-Ali Amiri, quoted by the official IRNA news agency, said a charge of "mohareb", meaning the accused "waged war against God and the country", had been dropped.
IRNA said this was the only charge carrying the death penalty in the case, which has aroused international concern.
Defence lawyers had previously said that an initial charge of "mohareb" had not been proved during the trial.
Eight of the 13 have publicly confessed to belonging to a spy ring for Israel, but the defence says these admissions have not been backed up by evidence in court.
Though the hearings have ended, Amiri told AFP that the court was awaiting an answer on an unspecified "important point" before the trial was officially closed.
Amiri at first said this was expected Thursday, but later corrected to Saturday. The verdict would follow a week later, and would also concern four Muslims charged with the Jews, he said.
Eight Muslims, whose identities have never been revealed but who are thought to be state employees accused of passing on classified information, were originally said to have been among the defendants.
Amiri said there was no reason for concern about the delay.