Stanley Tookie Williams, 51, was convicted 24 years ago of murdering a shop assistant and a family who ran a motel during robberies in 1979.
Williams, a founder of the notorious Crips gang, has never admitted the murders and is scheduled to be executed by lethal injection at San Quentin jail, north of San Francisco, next Tuesday.
During a 60-minute session behind closed doors on Thursday, lawyers for Williams asked Schwarzenegger to commute their client's sentence to life in prison without the possibility of parole.
On the streets outside, anti-death penalty campaigners gathered with banners reading "Save Stanley". They say that Williams is more valuable alive than dead, given his influence with young people and the message that he now espouses.
Rather than repeat arguments, which have failed in court, that Williams is innocent, defence lawyers argued that Williams has redeemed himself through his work in urging youths to avoid gangs. During his time in prison he has written a series of books aimed at children and urging them to steer clear of gang and drug culture, holding himself up as an example of where that can lead.
'Don't do what I did'
Peter Fleming, one of the defence lawyers, said: "Stanley Williams has been where these at-risk children are, and the whole thrust of his message is 'don't do what I did'. His message, whatever the result, is the message of peace."
Neither Fleming nor prosecutors would comment on how the meeting with the governor went, but the defence attorney did say: "I'm still frightened to death." Prosecutors in California and prison officials say that Williams is a poor candidate for clemency because he has not admitted to the murders and still has gang ties.
John Monaghan, the assistant head deputy district attorney in Los Angeles, said: "The evidence in this case is truly overwhelming. There are certain murders, not any murder, where an individual's conduct is just so abhorrent, the crime is so brutal, it simply justifies the ultimate punishment."
The defence team says that Schwarzenegger represents the last realistic chance to spare Williams's life after the California Supreme Court declined last week to stop the execution.
Ronald George, the chief justice, told Reuters after the ruling: "When we review death judgments we can review only for error. We cannot exercise that element of mercy which is properly considered as part of outside-the-legal-process function of a governor or a president in granting clemency or a pardon."
Nobel Peace Prize
Schwarzenegger's office expects a decision before Monday.
Supporters of clemency for Williams, including Jamie Foxx, the actor who played Williams in the film Redemption released last year.
On Wednesday, a university professor also resubmitted Williams's name for a Nobel Peace Prize. Philip Gasper, a philosophy professor at Notre Dame de Namur University in Belmont, California, said: "It's one attempt just to draw attention to the anti-gang work that Mr Williams has been doing."
Schwarzenegger has denied two clemency appeals since taking office in 2003. The last governor in California governor to grant clemency before an execution was Ronald Reagan in 1967.