An estimated 30,000 inmates in jails across California are participating in a hunger strike to protest against solitary confinement and other conditions they say amount to torture.

Prisoners refused meals for a second day on Tuesday in about two dozen jails, signalling what was thought to be the biggest protest of its kind in California's history.

The campaign is a ramped-up sequel to hunger strikes in 2011, which shone international attention on the state's troubled penal system but failed to wring significant concessions from authorities.

A group of inmates at the maximum security Pelican Bay state prison in Crescent City has organised the protest, saying they will starve themselves unless the California Department of Corrections and Rehabilitation (CDCR) agrees to meaningful negotiations.

At any one time, California holds about 12,000 inmates in extreme isolation, including some who have been in windowless boxes known as security housing units (SHUs) for decades. They are allowed out for an hour a day to exercise – some in a yard, others in a kennel-size cage.

Supporters say the strike is a legitimate response to cruel and inhumane conditions. "The use of prolonged solitary confinement is a form of torture," said Laura Downton, director for US Policy and Program at the National Religious Campaign Against Torture. "We stand with them in their call for five core demands."

The strikers have issued a number of demands, including the end to group punishment, an overhaul to the policy of identifying suspected gang members, an end to long-term solitary confinement, better education and rehabilitation programmes, and the provision of adequate and nutritious food.

The principal grievance is California's unusual policy of indefinitely putting suspected gang members in solitary and moving them back into the regular jail only if they identify fellow gang members.

The protest has united black, Latino and white inmates, including members of racist gangs. "It's phenomenal. They are coming together because they know in unity is where ultimate victory lies," said Dolores Canales, co-founder of California Families to Abolish Solitary Confinement.

"The mood is hopeful, but this also shows how hard things are. They are sacrificing the one thing that is given to them to keep them alive." Many family members on the outside have joined the strike, she said.

The Pelican Bay leaders had defied their isolation, and the supposed mutual loathing between racial groups, to organise the mass protest, said Laura Magnani of the American Friends Service Committee, a Quaker advocacy group. "Prisoners have to communicate and find ways to do it. They have a grapevine. It's amazing."

Inmates in two-thirds of the state's 33 jails, as well as four out-of-state jails, started refusing meals on Monday, said corrections spokeswoman Terry Thornton. Inmates are deemed to be on hunger strike if they skip nine meals. Authorities said that about 30,000 are classified to be taking part on the action.

Meanwhile, around 2,300 prisoners also refused to turn up for work or classes, some citing illness.

At its peak, the 2011 hunger strike, also led by Pelican Bay inmates, drew about 12,000 inmates in about 11 jails. It ended after authorities promised to consider reforms.

The California assembly held hearings, and the gang validation procedure was tweaked so an inmate would be deemed a gang member based on behaviour, not on association with other inmates.

But what inmates saw as insufficient change and follow-up prompted the new protest, which has been planned for months.

"Our decision does not come lightly," said a June 20 letter from the Pelican Bay leaders. "For the past two years we've patiently kept an open dialogue with state officials, attempting to hold them to their promise to implement meaningful reforms, responsive to our demands."

It said its leaders had participated in a mediation session – ordered by a judge in their class action lawsuit – but that authorities acted in bad faith.

"Thus we are presently out of alternative options for achieving the long overdue reform to this system and, specifically, an end to state-sanctioned torture, and now we have to put our lives on the line via indefinite hunger strike to force CDCR to do what's right.

"We are certain that we will prevail … the only questions being: How many will die starvation-related deaths before state officials sign the agreement? The world is watching!"

The start of the protest, though more than double the size of the previous one, has generated some local media attention but not made national headlines as yet.

The use of solitary confinement spread from federal to state penitentiaries, especially in California, which said gang violence behind bars required isolation cells to separate the "worst of the worst".

The California Correctional Peace Officers Association, a union representing 27,400 members, has defended their right to select inmates for solitary confinement and to determine the punishment's duration, saying it helps to tamp down violence.

Downton, of the National Religious Campaign Against Torture, said the policy caused psychological harm and worsened violence. "After 15 days in isolation the chemistry of the brain begins to change … leading to increasing rates of hallucinations, paranoia and self-mutilation. It has become a default management tool rather than a tool of last resort."