Amazon formed a consortium with J.P. Morgan and Berkshire Hathaway to figure out how to reduce health spend for its own employees. The company is also selling medical supplies into small doctors' offices and large hospitals alike, and is considering a push into the drug supply chain.

Cook acknowledged at the company's annual shareholders meeting in Cupertino, California, that the health-care sector, which is notoriously complex, doesn't always encourage new players to innovate. But he reassured shareholders that he views Apple as having a "great position," in the sector, by taking a more consumer-friendly approach.

Apple CEO Tim Cook talked up the company's ambitions in the health-care sector on Tuesday, hinting that it will move beyond wellness apps and devices, like its step-tracking Apple Watch.

Alphabet has an array of initiatives in the space, ranging from an anti-aging group called Calico to its health software and devices-focused unit, known as Verily.

The $3 trillion health sector represents such an enticing opportunity for health care players, as it's considered behind the curve when it comes to technology. There's also a growing trend of consumerization in health care, with Americans increasingly paying out of pocket for their health care rather than relying on employers or the federal government to pick up the tab.

Apple's iPhones now include software for consumers and health developers to access medical information. But it also has a business-to-business strategy, as its iPad and other devices are also widely used in the medical community, particularly among doctors.

To get beyond wellness, Apple will need to work with federal regulators going forward. Cook also said at the meeting that he's "not worrying" about whether the government will agree to reimburse its offerings.

Apple is already collaborating with the U.S. Food and Drug Administration for a pilot program to help the agency figure out how to regulate lower-risk digital health products. While it might not be getting widely reimbursed by insurers, it has locked down a partnership with health insurer Aetna to get discounted Apple Watches into the hands of its members.

Cook also mentioned the company's efforts to bring medical records to the iPhone. This product is still in beta, and only about a dozen hospitals are signed up, although the company has big ambitious to open this up more broadly to the entire U.S. health-care ecosystem.

"The more and more time we spend on this," explained Cook, "the more excited I am that Apple can make a significant contribution here.