"We demanded the death penalty for Ali Hassan al-Majid and the others," al-Faroon said in his closing statement to the court.
Majid is charged with genocide while the other defendants are accused of war crimes and crimes against humanity.
Some Kurds in Iraq welcomed the prosecution's request, calling it to a step towards justice.
"We don't want him to just be hanged. We want him to be chopped to pieces because he killed many innocent Kurds," Mohammed Ahmed, a 75-year-old farmer from Sulaimaniya said.
The other four defendants for whom the prosecution wants the death penalty are Sabir al-Duri, the former director of military intelligence, Sultan Hashim al-Tai,the former defence minister, Hussein Rashid al-Tikriti, the former deputy chief of operations for the armed forces, and Farhan al-Juburi, a former military intelligence commander.
But despite the prosecution's call for al-Duri to face the death penalty, Faroon said he had asked the court "on a personal level to show leniency" to the defendant.
He said the request came following appeals from the people of the central city of Karbala who say that "he had done significant humanitarian work when he was the governor of the city".
It is alleged that during the 1988 Anfal campaign Saddam's armed forces bombed and gassed thouands of Kurdish villagers.
Prosecutors say that 182,000 Kurds died in the mass slaughter.
The defendants have said Anfal, meaning "spoils of war", had legitimate military targets, namely Kurdish fighters who had sided with Iran during the last stages of the eight-year war with Iraq.
The trial has been adjourned until April 16, when the defence is to make its closing remarks.