The demand comes during a series of trials at the Denpasar District Court involving the so-called Bali Nine, a group of young Australians apprehended in Bali and charged with heroin trafficking.
The life imprisonment call is somewhat of a reprieve for Rush, as prosecutors could have asked for him to be sentenced to death by firing squad.
Prosecutors said a life sentence is justified as Rush damaged Bali's reputation ands was allegedly involved in a serious organised crime.
Reading part of a 92-page summary, prosecutors said while Rush has been polite and quiet in court, there are no extenuating circumstances.
Rush's lawyers immediately responded by saying they would continue to mount a defence as he does not deserve life in jail, and the onus of intent had not been proven by the prosecution.
The 20-year-old Brisbane man was caught at Bali airport with heroin strapped to his body last April.
In his defence, Rush has portrayed himself as a drug mule who was forced into the smuggling operation, facing death threats from other members of the gang.
Under Indonesian court procedures, prosecutors tell judges what punishment they think a defendant should get if found guilty.
While the calls are not binding on judges, they often do have a bearing on final verdicts.
Several other members of the Bali Nine are to hear what prosecutors have to say about their cases later this week.
All have been charged with drug smuggling - a capital offence in Indonesia.
The decision to call for life imprisonment for Rush was delayed for days, apparently caused by indecision within Indonesia's attorney-general office over what penalties should be handed down against the young Australians.
Meanwhile, the Australian Federal Court has refused to give four of the Bali Nine access to Australian Federal Police files to see if they have grounds to launch a court challenge against the force.
AFP Commissioner Mick Keelty said the decision shows that his officers acted lawfully in the case.
"The AFP has always insisted that we acted lawfully and the court upheld that and we also said we acted not only within the law but also within the ministerial guidelines," he said in Brisbane.
Lawyers for Rush, Renae Lawrence, Martin Stephens and Michael Czugaj said the AFP acted illegally in telling Indonesian authorities of the alleged drug activity, and its actions may have breached Australian law by exposing the four to the death penalty.
But the court said such a challenge is purely speculative.