Over 50 prisoners have needed medical care due to the strike so far as both sides struggle to reach an agreement.
Dozens of family members and supporters of the 385 California inmates on a weeks-long hunger strike urged Governor Brown to step in and resolve the protest.
The prisoners want changes to solitary confinement known as the Security Housing Unit or SHU.
St. Mary's College Professor Ronald Ahnen is ready with a mediation team.
"The conditions that they're being held in is torture," said Ahnen. "They're human beings. That doesn't give us the right, no matter what they did, it doesn't give us the right to torture them."
California has 4 SHU prisons, holding more than 4,500 men. The state calls those inmates 'the worst of the worst.'
Separated from the rest of the prison population to control gang violence, they generally get less food, fewer privileges and no phone calls until they can earn their way back to a regular cell.
Once with 12,000 participants at its peak, the hunger strike, which is defined as missing nine meals in a row, is led by a convicted murderer with alleged ties to the Aryan Brotherhood.
Todd Ashker's lawyers posted an interview on the Prison Hunger Strike Coalition website where Ashker is heard saying: "There's a core group of us who are committed to taking this all the way to the death, if necessary."
That worries Angie Gallegos of Santa Monica, who says her brother Victor has been in the SHU for 23 years, but she understands why he's doing it.
"He's buried alive," said Gallegos. "He's in a tomb. If he's been there 23 years, who would want to live another 23 years alike that?"
The Corrections Department insists conditions are not inhumane, pointing out inmates in the SHU are double bunked, get cable TV and daily contact with staff.
"As far as we're concerned, it's not solitary confinement," said Jeffrey Callison of the California Corrections Department. "Is it a great place to spend time? No, it isn't. But no prisons are."
No meeting with Governor Brown has been scheduled but protesters have submitted more than 70,000 signatures to his office calling for an end to solitary confinement. Celebrities like Bonnie Raitt and Jay Leno have also joined the call.
The state says it has taken steps in the last two years to improve conditions in the SHU.