"All the elements in the hands of the courts prove that a crime has been committed," said prosecutor Ahmed Ould Moustapha, who also called for the former leader's assets to be confiscated.
Aziz, 66, was president of Mauritania, a pivotal country between North Africa and sub-Saharan Africa, from 2008 to 2019.
He listened to the prosecutor's demand without flinching.
Ten other people, including two former prime ministers as well as former ministers and businessmen, are on trial with Aziz.
They have been accused of illicitly enriching themselves, abusing their functions and "influence peddling."
Aziz has maintained his innocence and said the trial, which began in January, is political and should be dismissed.
The prosecutor's closing arguments lasted about three hours and saw him request sentences of 10 years in prison against the two former prime ministers and two ministers, as well as the confiscation of their property.
For the other defendants, he requested five years in prison.
Abdel Aziz stepped down in 2019 after two presidential terms, and was succeeded by a former general, Mohamed Ould Ghazouani.
The inquiry began shortly after he left office, starting with a parliamentary probe in August 2020. He was charged in March 2021.
The probe focused on Mauritania's oil revenues during his presidency, the sale of state assets, the winding up of a public company in charge of food supplies and the activities of a Chinese fishing company.
Abdel Aziz, accused of piling up an estimated $67 million, says he is the victim of score-settling by rivals and has persistently refused to speak to the examining magistrate.
He has argued that he has immunity from prosecution under the constitution and has not denied being rich.