Third-quarter operating income fell 16 percent at Partners HealthCare System, the state's largest hospital and doctors organization, amid intensifying cutbacks from public payers such as Medicaid and Medicare, the government insurance programs for low-income residents and senior citizens. But even as its operating margin narrowed to 3.7 percent in the April-to-June period, from 5 percent in the same quarter last year, Partners chief financial officer Peter K. Markell said the health care system remains confident it can maintain a margin -- the share of revenue after expenses -- of between 2 and 4 percent going forward.