"We demand the maximum punishment for Saddam, (his half-brother) Barzan Ibrahim al-Tikriti and (former vice president) Taha Yassin Ramadan," Jaafar al-Mussawi said in court as he rested the prosecution case.
Saddam smiled from the dock as the prosecutor called for him to be sent to the gallows.
The prosecutor asked that charges be dropped against defendant Mohammed Azzam Azzawi, a former official of Saddam's ruling Baath party with responsibility for the Dujail area, and that he be released.
Al-Mussawi asked the court to show leniency to three other local Baath party officials - Ali Daeh Ali, Abdullah Khadem Ruweid and his son Mezhar Abdullah Ruweid.
The prosecutor said he would leave it to the court to decide on the appropriate punishment for Awad Ahmed al-Bander, the former chief judge of the revolutionary court and deputy head of Saddam's office.
The trial was adjourned until July 10 when the defence team will make its closing arguments. The five-judge panel is then expected to recess the court to consider its verdicts.
Saddam Hussein and seven former members of his government all face charges of crimes against humanity.
The charges relate to the deaths of 148 Shia civilians in the town of Dujail, following a bloody crackdown after an assassination attempt on the former Iraqi leader in 1982.
All eight defendants were in the dock for Monday's hearing, although some of the defence lawyers were absent.