Madoff, 71, a former non-executive chairman of the Nasdaq stock exchange, pleaded guilty in March to charges that his secretive investment advisory operation was a multibillion-dollar scam - the largest in US history.
Madoff could spend the rest of his life in prison when he is sentenced on Monday.
Federal prosecutors want Madoff to be sentenced to 150 years in prison for orchestrating perhaps the largest financial swindle in history.
Madoff's lawyer has said his client should serve only 12 years.
"The sheer scale of the fraud calls for severe punishment," the prosecutors wrote in response to a defence motion seeking lighter punishment.
Federal sentencing guidelines allow for the 150-year term, prosecutors said. Any lesser sentence, they added, should still be long enough to send a forceful message and "assure that Madoff will remain in prison for life".
At the time of Madoff's arrest, fictitious account statements showed thousands of clients had $65bn. But investigators say he never traded securities, and instead used money from new investors to pay returns to existing clients.
Prosecutors said on Friday that the total losses, which span decades, haven't been calculated. But 1,341 accounts opened since December 1995 alone suffered loses of $13.2bn.