Peter Mangs, 40, should be punished "at the level of a life sentence," prosecutor Solveig Wollstad said in closing arguments on the penultimate day of the trial at the Malmö District Court in southern Sweden.
She said however she would refrain from making a final recommendation until after the court rules Tuesday on whether Mangs should undergo a psychiatric evaluation to determine if he should go to prison or be sent to a mental institution.
Mangs was arrested in November 2010 after a massive manhunt following a string of shootings against people of immigrant origin that gripped Sweden's third largest city with fear.
He has been charged with killing two men of immigrant origin, aged 23 and 66, in 2003 and a 20-year-old Swedish woman who had been sitting in a car with an immigrant man in 2009.
He has also been charged with 12 attempted murders in which he fired numerous shots with his Glock 19 pistol at homes, businesses and cars as well as out in the open, seriously injuring a number of people and coming close to killing many others.
Mangs "has ruthlessly ruined many people's lives. He is completely indifferent (to their suffering). It is clear that this has been a lifestyle for Peter Mangs," Wollstad told the court, according to the Aftonbladet daily.
Mangs has protested his innocence, with his defence arguing there are no fingerprints or DNA linking him to the crimes, and trying to cast doubt on forensic evidence showing the bullets were fired from his gun.
But according to public radio, Mangs has confessed to acquaintances, prison guards and a psychiatrist that he was behind several of the shootings.
Wollstad insisted the racist nature of the crimes should influence the court to give Mangs a harsh punishment.
"It cannot be a coincidence that all of the victims, except two, were of immigrant origin," she told the court, according to the TT news agency, saying that Mangs "calls people of immigrant origin monkeys."
In Sweden, people sentenced to life can request after 10 years behind bars that their sentence be reduced, and few people serve much more than 20 years.
The defence will give its closing arguments Tuesday.
Mangs denies 19 of the 20 charges against him, but has confessed to one count of vandalism for having fired a shot through a shop window.