The board of the $356 billion California Public Employees’ Retirement System voted against divesting from private prisons, rebuffing pressure from state lawmakers to drop the holdings.

Board members voted Monday to support a staff recommendation focused on engaging companies to change, while leaving open the possibility that divestment could be evaluated again at a later time.

“It’s shameful the government contracts out private prisons,” board member Jason Perez said at the meeting in Sacramento. Even so, he added, “That’s not...