The government has implemented reimbursement reforms under the Affordable Care Act that aim to cut costs, but with private employers and their workers footing the bill for nearly half of the nation's $2.7 trillion in health-care spending, the council CEOs think that by working together companies can leverage their market power to do more.
"We can all make these incremental changes that we've all made, we can continue the wellness plan, but the question is really with long-term thinking—how do we drive to a long-term change?" said council member Brian Moynihan, CEO of Bank of America.
The CEOs are challenging business leaders not just to improve care for their companies, but their communities and the nation's health system.
Telecom provider Verizon, which spends $3.5 billion a year to provide coverage for 740,000 workers, retirees and dependents, is focused on leveraging mobile and interactive technology to widen access to lower-cost care both for its employees and for community health programs.
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"We need to use the power of that technology to transform health care. Things like telemedicine, electronic health records," said Verizon Co-Chair and CEO Lowell McAdam. "All of these innovations can help people take charge of their health and improve their quality of health and their lives."
Not coincidentally, health IT is in an increasing part of the telecom giant's business. Verizon was one of the contractors that worked on the federal HealthCare.gov insurance exchange last year.
For Walgreen President and CEO Greg Wasson being a health-care provider means having a better perspective about what really works to improve the health of both the company's employees and its customers. His strategy starts with an incentive to change.
"Proactive benefit designs that encourage healthy behavior—trying to mitigate cigarette smoking, help people with weight loss—which are the top two causes of disease in this country," said the drugstore chain chief.
While Walgreen promotes smoking cessation, Wasson and the company's board have so far resisted calls from health advocates to stop selling tobacco products in its drug stores. Rival CVS Health stopped selling tobacco earlier this month.
Some health advocates may also take issue with Coca-Cola's role on the council, and the soft drink maker's commitment in the report to support community programs to combat childhood obesity.
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The Bipartisan Policy Center's Marchibroda said the report is meant to spark a dialog about health care, and to encourage large and small business leaders to help bring about change.
"This was meant to be not something exclusive to the CEO council," she said. "We hope hundreds of thousands of employers will step forward and also make commitments in the coming month."
—By CNBC's Bertha Coombs