Beate Zschäpe, 42, is co-accused in the 10 killings carried out by the other two members of the self-styled National Socialist Underground (NSU), Uwe Mundlos and Uwe Boehnhardt, between 2000 and 2007.
Zschäpe for years lived in hiding with Mundlos and Boehnhardt, who shot dead eight men of Turkish origin, a Greek migrant and a German policewoman before the two died in an apparent suicide pact after a botched bank robbery in 2011.
After the men's deaths, Germany was shocked to discover that the nationwide killings - long blamed by police and media on migrant crime gangs and dubbed the "döner (kebab) murders" - were in fact committed by a far-right cell with xenophobic motives.
Prosecutor Herbert Diemer told the Munich court on Tuesday that Zschäpe shared the "fanatical" world view of the two men and their aim to spread fear and terror among immigrants with random murders.
He pointed to the severity of the crimes and called for the maximum life term, which under German law means a prisoner spends 15 years behind bars, followed by indefinite preventive detention on security grounds.
Prosecutors charge that Zschäpe was an NSU member and aided the crimes, also including two bomb attacks and 15 bank robberies, by covering the men's tracks, handling finances and providing a safe retreat in their shared home.
The mammoth trial - with 95 victims' relatives listed as co-plaintiffs - has so far lasted more than four years and heard almost 600 witnesses.
A verdict is expected in several months' time in the trial where Zschäpe is in the dock together with four suspected NSU supporters.
Zschäpe has denied guilt and described herself as a passive and innocent bystander to the bloody crimes.
She has admitted only to an arson charge, having torched the trio's common home after the men died, and of then distributing a DVD in which the group boasted about the killings in a film set to a comical Pink Panther theme.
She broke her silence only a year ago, telling the court that she was involved "neither in the planning nor the execution" of any crimes, and that she was "horrified" to learn about them afterwards.
She admitted that as a youth in the former communist east Germany, after the fall of the Berlin Wall, she had "indeed identified with nationalist ideology".
But she insisted that "today I judge people not by their origin and political affiliation but by their behaviour".
The random discovery of the NSU in 2011 deeply embarrassed German authorities, exposing police and domestic intelligence flaws and raising uncomfortable questions about how the cell went undetected for 13 years.
German security services faced withering criticism for only associating terrorism with far-left or Islamist groups, not neo-Nazis.
A parliamentary panel in 2013 blamed institutional prejudice among security services for failing for years to solve the series of assassination-style shootings committed with the same Ceska handgun.
It also criticized excesses in the use of paid undercover informants, including violent leading neo-Nazis, who fed the money they received from the state back into their racist and militant organizations.