"So we may spent a bunch of time getting one piece of it right, and testing various things to see what works," he added.

"This is an absolute critical issue and all of us have a long-term view and we've been through the amount of money spent on fraud, administration, end-of-life, the misuse of drugs," and others, Dimon told CNBC's Wilfred Frost. "I'll remind people that Jeff Bezos, when he started Amazon, he might have had visions about the 'everything store,' but he started with books. And he spent 10 years getting books right."

J.P. Morgan Chase's CEO Jamie Dimon said Monday that his partnership with Jeff Bezos and Warren Buffett to improve health care for employees will likely start small, akin to Amazon's small-scale operation during its first few years.

Dimon, 62, is the longest-tenured of CEOs leading a major U.S. bank. , , and announced earlier this year a partnership to cut health-care costs and improve services for their U.S. employees.

The companies, which employ more than 1.1 million workers combined, will launch an independent operation that's intended to be free from profit-making incentives. The chief executive added that the joint venture upset some of J.P. Morgan's clients, but said that if some chose to leave as a result of the initiative "so be it."

The new company's goal at first will be to target technology solutions to simplify the health-care system.

"I want to do a better job, and we're going to put more brainpower, more capability to figure out how we can make you healthier and happier with better satisfaction," Dimon added, noting that approximately 20 percent of U.S. gross domestic product is spent on health care. "We're totally in-line with Jeff Bezos and Warren Buffett – Amazon and Berkshire."

The business trio tapped renowned surgeon and author Atul Gawande in June to lead the joint venture in the hopes to slash cost. Gawande, an outspoken critic of the industry's medical practices, has argued against prolonging a poor quality of life for the elderly and terminally ill, saying health care institutions often deprive patients of independence and quality of life.

"We think together we have the right people, a long-term view, we're not profit-seeking, and that we can do what we're doing a lot better," Dimon said. "We don't expect progress in the immediate future – like a year or two – but if we come up with some great stuff, we're going to share it with everybody."