The demand also applies to former Interior Minister Habib el-Adly and six other former security chiefs.
More than 800 protesters were killed during an 18-day revolt before Mr Mubarak was ousted on 11 February.
“Any fair judge must issue a death sentence for these defendants,” prosecutor Mustafa Khater said, according to AFP.
“He [Mubarak] can never, as the head of the state, claim that he did not know what was going on,” chief prosecutor Mustafa Suleiman told the court.
“He is responsible and must bear the legal and political responsibility for what happened”, he added.
Given the severity of the charges, the demand for the death penalty does not come as a surprise, but many Egyptians will be shocked to hear the demand put so bluntly for the first time in the trial, the BBC’s Jon Leyne in Cairo reports.
However, whether Mr Mubarak will be executed or even convicted is another question entirely – the prosecution has complained of a lack of co-operation from the interior ministry in producing evidence and the case has been weakened by a key witness changing his testimony, he adds.
The prosecution says it has taken testimony from 2,000 witnesses, including police officers who discussed orders from above to arm police with automatic rifles and shotguns to use against protesters.
Some of Egypt’s most powerful figures have testified since the trial began in August.
The head of the ruling military council, former Defence Minister Field Marshal Mohammed Hussein Tantawi, told a closed-door session in September that Mr Mubarak had never given orders to shoot protesters.
The trial has now been adjourned to 9 January, when the defence is expected to present its case.
Mr Mubarak’s two sons, one-time heir apparent Gamal and Alaa, face corruption charges in the same trial.
